1. A blanket (or toy) carried by a child to reduce anxiety
Stems from the Peanuts comic where the character Linus always had his blanket with him.
2. (informal) anything that an adult person uses to reduce their anxiety
This phrase can also be used to indicate a male friend whom a girl has no romantic interest but uses him to to cock block other males at parties, dances, or other events.
Whenever my boyfriend doesn't want to go out dancing, I take Kyle to keep the other guys away. He's sort of my security blanket.