For years, the abbreviation "MBFR" has been a mysterious term that pops up occasionally on the inside pages of newspapers - usually to be ignored by baffled readers.

Within the past two weeks, though, MBFR - shorthand for "mutual and balanced force reductions" - suddenly has become the subject of public discussion by both President Carter and Soviet President Leonid I. Brezhnev.

It's still too early to tell where this talk might lead. But the interest shown by the two leaders could be a sign that MBFR soon may be taking place alongside that other symbolic abbreviation. SALT (for "strategic arms limitation talks"), as an important element in the quest for East-West detente.

MBFR is the little-known kid brother of SALT, whose goal is U.S.-Soviet agreement that would impose ceilings on each country's stockpiles of such nuclear weapons systems as intercontinental missiles and long-range bombers.

In contrast, MBFR deals with another facet of the gigantic military machines that have been built up by East and West to hold each other in check through a so-called "balance of terror." It is concerned with the ground forces of conventional warfare - the foot soldiers and the tanks and guns that are their supporting weapons.

Specifically, MBFR involves an attempt to negotiate a reduction in the ground forces that the two big military alliances, the North Atlantic Treaty Organization for the West and the Warsaw Pact on the communist side, have poised against each other in Central Europe.

The idea isn't a new one. It's been kicking around for roughly a decade and has actually been the subjects of formal negotiators in Vienna for almost five years. But, until a few days ago, these talks had been stuck on dead center and seemed to be going nowhere.

What suddenly changed things was the Warsaw Pact's initiative in putting forward new proposals that, on the surface at least, seemed to go a long way toward narrowing the gap dividing the two sides in the Vienna talks.

To underscore that point, Brezhnev, during a major speech in Minsk June 25, characterized the proposals as a major effort by the communist side to break the deadlock and called on the West to assess it very carefully. Referring to the years of stalemate in Vienna, Brezhnev said: "Let us get down to business at last."

The following day, Carter, in a nationally televised news conference, responded in cautious but clearly upbeat terms. The Soviets, he said, had acted "in a very affirmative way"; and Carter added: "I would say it is a step in the right direction, and we will pursue it."

In private, Carter administration sources say the Soviet proposals, while outwardly seductive, contain what could be a number of cleverly disguised booby traps for the West.

For Washington and its NATO allies, these sources add, the necessary next step must involve a lot of careful analysis and probing to determine whether the communist proposals are a snare for the unwary, a mere propaganda ploy or a genuine springboard for further bargaining that will finally get the force reduction talks moving.

Underlying this caution is awareness of the various twists and turns that the MBFR talks have taken over the last several years. Originally, they grew out of the complex, interwined series of diplomatic tradeoffs between East and West that, in the early 1970s, became known as detente.

At first, MBFR's main backer was the Nixon administration, which found itself fighting pressures from Congress for substantial cutbacks in the approximately 200,000 American troops stationed in Europe.

As a counter to this congressional pressure, the Nixon administration seized on the idea of negotiating troop cuts with the other side. It would be unwise and damaging to NATO's defenses, the argument went, to make a one-sided withdrawal of U.S. forces when they could be used as a bargaining couter to force parallel cuts in the Warsaw Pact forces.

Initially, the idea didn't spark much enthusiasm either on the communist side or among Washington's European allies. Among the other members of NATO, the feeling was that any withdrawal of U.S. troops automatically would work to Moscow's advantage - an attitude summed up by a British defense minister, Lord Carrington, who wryly defined MBFR as "more battalions for Russia."

"Moscow's wariness was grounded in apparent concern about the ability of East European bloc partners to maintain internal stability in their countries without the presence of sizable numbers of Soviet troops. One of the chronic unknowns of the East European scene is how the Polish or East German armed forces would react if their countries ever became affected by anti-Soviet turmoil.

Still the U.S. position ultimately prevailed. The NATO allies were brought into line, and Moscow agreed to at least talk about the subject as the price for western participation in the Soviet-backed Helsinki Conference on European Security and Cooperation.

Finally, after a great deal of complicated skirmishing, the Vienna MBFR talks formally got under way in November 1973. It was agreed that the negotiations would encompass the ground forces of those countries in the two alliances with troops on Europe's Central Front.

On the NATO side, that meant the United States, West Germany, Britain, Canada, the Netherlands, Belgium and Luxembourg. For the Warsaw Pact, the countries involved were the Soviet Union, East Germany, Poland and Czechoslovakia.

Since then, though, the two sides have been unable to agree on anything else. Until recently, the principal sticking point was the communist side's refusal to accept NATO's insistence that any cuts should be made according to an "asymmetrical formula" - one that would see the East take out more troops than the West.

NATO says these kind of cuts are necessary because the Warsaw Pact has vastly superior numbers, both in men and tanks, and the natural advantages of geography. In any mutual cuts, Soviet troops would have to pull back only relatively short distances behind their national borders, while the American forces would be withdrawn clear across the Atlantic.

As a result, the West repeatedly has called for cuts in two stages - the first involving just the United States and the Soviet Union and the second bringing in the other countires - that would bring the combined forces of both alliances down to a common ceiling of equal sizes.

For years, that appeal was rejected by the Soviets, who spurned both the idea of asymmetry and the western argument that the forces involved should be considered as integrated units. Instead, the Soviets kept proposing reductions based on percentages of each participating country's forces - a move aimed at constricting the 350,000-man. West German land army, which is the largest NATO force in Central Europe.

In the face of this prolonged impasse, the MBFR talks gradually dwindled in importance, even from the standpoint of Washington. As congressional calls for cutting the U.S. forces abated. U.S. officials, finding the pressure off, began to view MBFR as a useful but relatively low-priority project to be tended by low-level bureaucrats.

Then, late last year, NATO interest began to rise again, largely as the result of pressures from West German Chancellor Helmut Schmidt. He took the position that a SALT agreement, if successfully achieved, would mean such fundamental changes in the European strategic balance that Western Europe's defense would also require considerable adjustments in conventional forces.

Schmidt's prodding resulted in a new western initiative, which was unveiled in April. Basically, it called for a first-stage reduction that would see the Soviets withdraw 68,000 soldiers and 1,700 tanks, while the United States would pull out 29,000 soldiers and 1,000 tactical nuclear missiles.

To the surprise of the West, the Soviets responded recently with a counteroffer that one Carter administration official says "absorbs for the first time quite a lot of the western approach."

In essence, the Soviet offer accepts the NATO concept of a common ceiling of 700,000 men for each side. To reach that point, the Soviets proposed an initial cutback of 30,000 of their troops and 14,000 American soldiers; a second-stage cut of 25,000 Soviets and 10,000 Americans, and reductions among the other countries that would eventually trim the overall Warsaw pact forces by 105,000 men and NATO by 91,000.

Recently, the Soviets added another sweetener to their proposal by dropping their long-standing demand for country-by-country ceilings on forces stationed on the Central Front. Instead, the Warsaw Pact said it would settle for assurances that no country with forces in Central Europe would be allowed to reinforce them above their present manpower levels.

These were the proposals touted by Brezhnev and blessed by Carter as "a step in the right direction." But U.S. officials working in this area, while encouraged by the apparent Soviet acceptance of asymmetrical cuts leading to a common ceiling, say a lot of important questions still must be answered.

Their principal problem involves the arithmetic of the Soviet plan, or more specifically, the figures on which it is based. The Warsaw Pact insists its combined ground forces number 805,000, while NATO estimates them at more than 950,000 - a difference of roughly 150,000 men.

Thus the Soviet contention that it can draw the Warsaw Pact forces down to 700,000 by a cut of 105,000 men. But, if NATO's figures are correct, the communist side would have to pull 250,000 men to reach a 700,000-man ceiling.

As a result, U.S. sources say, NATO has no intention of proceeding on the basis of Soviet figures.Instead, they add, there will have to be a lot more Soviet give on exchanging troop data before it can be sure that the communist side isn't using its common-ceiling proposal as a device for secretly maintaining superior forces.

In addition, the sources say, the Soviet proposals about keeping each country's forces at present levels still amount to a form of national ceilings and, as such, is almost certain to prove unacceptable to West Germany, whose territory forms the western front line of the confrontation area.

Sitll, despite these cautions, administration sources say they think the Soviets are making a serious attempt to get the MBFR talks moving. The reason, they speculate, probably is grounded in Moscow's desire to demonstrate anew its commitment to detente, particularly in regard to Western Europe which would be affected most directly by changes in Central Front military status quo.

The next step, the sources say, is for the West to pinpoint the flaws and unacceptable features of the Soviet proposals, prepare specific counteroffers from NATO and then take them back to Vienna bargaining table to see if the communist plan is negotiable. It will be at that point, one source says "that we'll find out whether MBFR finally is ready to sprout wings and start to fly."