Their relationship: Poor Marty just has bad timing. He arrives in Rory's life when she really needs a friend in college more than a boyfriend (especially after the sting of Jess disappearing from her life). And when she's ready for a relationship again, Dean is back in the picture. By the time THAT falls apart, Logan's already on the scene.
Why he's important: Marty is honestly a very sweet guy; he simply gets stuck in the friend zone. He's Rory's first real close male friend, and their relationship goes the way that so many male-female friendships do. When the truth about how Marty feels about Rory finally comes out (and she admits her feelings for Logan), their friendship is over. He shows up in the final season, but their friendship never gets back on track. You're sorely missed, Naked Guy.