Can someone explain Modem's and Routers to me please?

[Jorge]

So I just recently installed internet into my home. I went with Time Warner (there customer service sucks) but there price is good. So they gave me a modem/router in 1. The coaxial wire goes directly into the router and sends out the signal. I get decent signal with my current router, but I want greater coverage to my rooms. I feel the router they provided me is just some cheap rotuer. Now here's what I want to do. I want to buy a new router specifically this one Xtreme N Wireless N Gigabit Broadband Router and I think I'm going to need a modem to connect to it correct? So I connect the coaxial wire to the modem, then connect the modem to the new router via ethernet cable? So here's my question, will I need to buy a better modem to get optimal speeds as well? I am buying a high end router, but does the modem need to be high end as well??