A wedge is a block of wood that keeps a door propped open, or a problem that pulls people apart, like the jealousy that drove a wedge between two friends.
Wedge means "triangle-shaped." Pieces of pie are wedges. So are tortilla chips. In some parts of the country, a sandwich on a long roll is called a wedge, or a wedgie, while in other places, it's a hoagie or sub. Just about everywhere, the wedge you get in the schoolyard means your underwear are pulled up between your butt cheeks, which is consistent with the verb form of wedge: to squeeze into a tight space.