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.

An object or act that assures one of safety and security.
This phrase was first derived from the blanket a characket from Peanuts(Charlie brown) always had with him. If memory serves me right a US Present coined the phrase.

Something put on or given to a victim after a traumatizing event.

A security blanket is a blanket that young kids have for security.
It originates from a character in the comic strip Peanuts, named Linus van Pelt who always had a security blanket with him.