IN its sum and its parts, the Democratic nomination race took a progressive turn in this week's Illinois primary. First the sum: The race certainly has not proved the yawner it might have been had Walter Mondale left his opponents packing their bags for good after the February Iowa caucuses. Here it is spring and a vigorous three-way contest is still running - one that could go all the way into summer.
Some argue that a heated nomination contest plays up the divisions within the Democratic coalition, making it more difficult to win in the general election. A party that embraces conservative-liberal tensions, its own Mason-Dixon line rivalries, pro-labor and open-shop ranks, even competing racial and ethnic blocs of voters, has a lot that divides it. A front-runner usually uses the close-the-ranks-early argument to help stifle any challenge.
But a nomination contest also should help air these differences, find the strengths of the competing factions and ideas, try out lines of appeal to swing voters as well as the party faithful. The merits of uniting early against a common opponent, in this case the Reagan Republicans, are not enough to warrant prematurely capping off a party's ferment. This could lead to a false peace. And particularly in 1984, after a defeat in 1980 when many Americans thought the party and its leaders had run out of stamina and ideas, the Democrats need to show they can muster genuine leadership fervor.
Now the parts: Each of the candidates proved something positive. The overall Illinois outcome - Mondale 41 percent, Hart 35 percent, Jackson 20 percent - was reasonably close. Mondale showed he had about regained his stride. His sense of humor now shows through his earlier caution and reserve. He opened his campaign a year ago by claiming, ''I am ready.'' Evidently a lot of Democratic voters didn't agree with him - or at least they weren't ready to take his word or accept his certification by the party establishment. By having to stand up against Gary Hart and Jesse Jackson, Walter Mondale is having to show whether he has the right stuff to represent the world's most powerful nation when it is tested.