I thought an adapter was needed for wireless internet...?

Forgive me, I know zip about laptops and wireless networks, etc. I was told before I bought my new laptop that I needed to buy an adapter along with the router in order for my laptop to connect to the Internet. But I'm on the Internet now and my Linksys adapter isn't plugged in. When I first used the computer it wouldn't connect without the adapter or ethernet cord. So how is it connecting right now? Should I return the adapter or will I need it for something else?