Some 25 months ago, when the Senate was weighing an extension of the Voting Rights Act, the Rev. Jesse Jackson came here to tell of "funny business" going on in Mississippi.

The state capital had annexed a white suburb and moved to at-large elections, a twin strategy whose most obvious effect was to dilute the influence of the growing black vote. There were Mississippi counties that requried "double registration"--in the voter's hometown and also in the county seat --a burden that could mean a round trip of 100 miles or more, and a special hardship on low- income voters.

Then, after telling the Senate Judiciary Committee of these and other barriers to black registration, he complained to the Justice Department, even threatening to bring suit to force the department's Civil Rights Division to live up to is charter and do something about the problem.

Last week, William Bradford Reynolds, Justice's assistant secretary for civil rights, ordered federal examiners into five Mississippi counties to facilitate the registration of black voters there.

What happened in the interim? Just this: Jesse Jackson persuaded Brad Reynolds to come to to Mississippi and hear for himself what was going on. Reynolds spent two days there last week, listening to the violations that Jackson had complained about in May 1981, and of other efforts to intimidate and discourage black registration.

He was shocked, he said, at what Mississippi blacks told him during a tour led by the president of Operation PUSH. "I heard about discriminatory redistricting," he told a Washington press conference last Thursday. "I heard about access to the circuit clerk being denied. I heard about intimidation at the ballot box. And I heard about difficulty with annexation." And he was so moved by what he heard that he ordered the federal registrars to Mississippi to do what they could in the short time remaining until the statewide primary on Aug. 2.

Jesse Jackson, who is still flirting with the possibility of a run at th presidency, is pleased. "It's not just Mississippi we're talking about, but all through the South black voters can make tremendous difference. With anything close to full registration, we have the potential for gaining another 15 or 20 black seats in the House."

But for that to happen, blacks will have to become politically active, Jackson says, and that entails a lot more than just voting. "To vote for candidates without having a role in deciding who the candidates will be is to come in at the tail end of the process.

"The significance of what we have demonstrated to Brad Reynolds is that you cannot have full political participation if you cannot vote, but you cannot get people to vote in numbers approaching their real potential unless they have a role in shaping slates, or even being on slates. That's what we were trying to get Mr. Reynolds to understand." 2 Jackson must be a first-rate teacher. Within hours of Reynolds' arrival in Mississippi, this stern-face Reagan conservative was linking arms with "the Country Preacher" and singing "We Shall Overcome."

Still you have to wonder at Reynolds' dramatically changed attitude with regard to a series of unchanged facts of Mississippi political life. One explanation is cynically political: that the Reagan administration, stung by the drumbeat of complaints that it is unconcerned about racial discrimination, wants to prove it cares--if not to to attract black voters at least to make itself acceptable to nonracist white voters.

Another explanation is that Reynolds, like many members of the Reagan administration, including the president himself, cannot understand racism until he sees it personalized.

He had heard the reports, but, as with so many horror stories, maybe you just had to be there.