Kal-El's blanket is the blanket that Kal-El was wrapped in when he was a baby being sent to Earth. It is later used by Kara Danvers, as part of her Supergirl suit as a cape.
Originally being the cape that the baby Kal-El was wrapped in when being sent to Earth, it was later given to James Olsen by Kal, to give to Kara Danvers to use as a cape.
DC's Legends of Tomorrow
Adventures of Supergirl