What is a wireless router and how do I know if I can use one with my laptop?

I just got high speed internet via satellite after years and years using dial up and cause of the rural area I live in that was the one and only option. I have heard about routers like the DIR-160 and I don't know exactly what they are or how they work and wanted to know if I could use one (like the one above) with my laptop. What exactly is a router and what does it do, or how does it work? I am using Windows XP SP3 IE8. Thanks.