When you swathe yourself in a blanket, you are wrapping or swaddling yourself up in it. Swathe a baby up and you're creating a little cocoon where she can sleep.
Sometimes spelled "swath," swathe is commonly used to talk about how you wrap up a baby in a soft blanket. The verb can also refer to binding a wound with bandages; as a noun, a swathe is a long strip or bandage to protect a wound. Swathe derives from an Old English word, swaþian, which means "to wrap."