To molder is to disintegrate or rot. If you store your books in the damp basement of your uncle's house, they're sure to molder.
Things molder when they're neglected or left to fall apart or become rotten. A ripe peach left on the counter will eventually molder, and even a person might molder, abandoned to grow old all alone in a remote rural house. You can see the word mold when you look at the verb molder, and in fact that's its origin, specifically the old verb form of mold, which is related to the Old Norse mygla, "grow moldy."