Batting is the soft, plush material on the inside of a blanket or quilt. When you make a quilt, you sew the front to the back with a layer of batting in between.
Batting is sometimes called wadding in the UK. It's usually made of cotton, and it adds thickness and warmth to a blanket. You might see batting used as imitation snow in a department store window, as well. The word comes from the now-obsolete bat, "felted mass of fur or wool," from the idea of "beaten" or "batted" fabric.