A wad is a bundle or lump of something, like the wads of chewing gum you'll find if you look under your chair at school. Yuck!
You can also call a wad a bundle, clump, or ball — most office trash cans contain wads of paper, and making a pillow involves stuffing it with wads of cotton or polyester material. Wad is also a verb, like when you wad up a damp hand towel and throw it in the laundry hamper. Etymologists guess that the Old Norse word vað, or "cloth," is the root of wad.