Pad has several related meanings, all connected to the idea of soft material or adding something extra:

1. A cushioned surface or piece of material. A knee pad protects your knee when you fall while skating. A mouse pad gives your computer mouse a smooth surface to roll on. Football players wear shoulder pads to cushion impacts. When you put a pad under a hot dish, you're protecting the table from heat.
2. Paper sheets attached together, like a notepad or sketch pad. Artists draw on large pads of paper, and people write grocery lists on small notepads by the phone. These pads make it easy to tear off one sheet at a time.
3. To add extra material to make something thicker, softer, or longer. A writer might pad an essay by adding unnecessary sentences to reach a word count. Someone might pad their coat with extra layers on a freezing day. When you pad across the floor in your socks, you're walking softly and quietly, like a cat padding around the house.

The word can also mean a place where someone lives, though this usage is fairly informal: “Come over to my pad after school.”