If you and your boyfriend split, you are no longer together. If your pants split, they come open at the seam. If both of these happen in the same day, split! (Get out of here!)
Split means to come apart or rip in two. It can be used as a verb "let's split the apple in two" or as a noun "be careful to step over the split in the earth left by the quake." It implies some violence. When firemen split open your door, they need an axe to do it.