The simple story of Maine's Democratic caucuses is that President Carter beat Sen. Edward M. Kennedy in Kennedy's backyard.

But the story is not quite that simple. A month ago, before Carter's smashing truimph in the Iowa caucuses, a Kennedy defeat in Maine would have been devastating. Even after Iowa, Kennedy said he would have to win Maine and New Hampshire to keep his candidacy alive.

He did not win Maine, but his candidacy is more alive today than it was a week ago. A poll released last Friday had given Carter a 19-point lead in Maine, but the president's final margin in Maine will be barely half that.

Maine was a victory for Carter, but not one that he and his advisers can savor. The results only add to the importance of the voting in the New Hampshire primary 15 days from now.

Maine also gave some life to the candidacy of California Gov. Edmund G. (Jerry) Brown, who spent last week campaigning there. Using an antidraft, proenvironment message, he brought out enough supporters to give him a respectable if distant third place.

This was the first time the Democrats held all their town caucuses on the same day. The Republicans are sticking to the traditional system of allowing towns to hold caucuses over a six-week period, which ends this year on March 15.

The results in Maine were also another victory for the election process.As in Iowa, the turnout far exceeded that of 1976 and even the expected turnout for this year.