To propagate is to be fruitful and multiply, by the usual routes of reproduction, or by spreading something around — like a rumor.
Propagate comes from the Latin word propagare, which means "to reproduce plants, breed." Plants love to propagate, especially when someone with a green thumb starts off with a jade plant stem in water and ends up with a garden full of the succulents. Plants aren't the only things to propagate like bunnies: in some apocalyptic movies, a virus propagates quickly, killing almost everyone in the world. Sound and light can also spread, or propagate, through the air.