WHAT IS IT that Americans want of Mikhail Gorbachev, anyway? An accomplished television manner? Personal affability? Professional competence? Command of the basic material? All these things were in evidence in the Soviet leader's interview with NBC. But they hardly slake American curiosity. We suspect that most people were peering at the broad, patient, intelligent face, sifting the words, for a sign that behind the warming atmosphere of the summit there lies a firm basis for steadying a relationship that has seen all too many turns and perils. Is there such a sign?

Certainly Mr. Gorbachev contrived an impression that he wants a successful summit. On strategic defense, he stated a more modest position that may approach the more modest one the Reagan administration has been moving toward -- positions that look to major early reductions in strategic offense. On conventional arms, he hinted at a flexibility that could ease anxieties stirring in Europe as a result of the treaty eliminating medium-range missiles, itself a pioneering accord that is due to be signed next week. On Afghanistan, a test of Soviet interest in reasonable global conduct, he kept alive the opening for a Kremlin retreat that has always been the first requirement for a settlement.

Still, most of us were looking for more than positions on issues, central as these are. There is a feeling in the air that Ronald Reagan and Mikhail Gorbachev, unlikely pair, have created a promise whose realization depends greatly on the relatively young man currently at the Kremlin helm. On this score the interview was not so reassuring.

Mr. Gorbachev has the brainpower, but it has not so far been matched by the breadth of experience that might let him shed a characteristic Soviet provincialism. He has some cartoon ideas about America and a hesitation to address before a Western audience the very shortcomings of Soviet society that prompted his ''restructuring.'' To take Western interest in emigration as a trick to steal Soviet science would be laughable if it were not so wrong and mean. To present the Afghan crisis as ''first and foremost'' the result of outside interference is, at best, misleading and evasive.

On television, Mr. Gorbachev can show an undeniable restraint and poise, but these qualities tend to fade when the heat is turned on. That leaves American viewers to conclude that Mr. Gorbachev is tough -- which no one doubted, but which is hardly enough in itself to sustain the improved relationship both sides presumably are reaching for. So much for the televised Gorbachev. Now comes the real one.