I looked it up on wikipedia and it didn't really speak to me since I'm not knowledgeable in computer servers.

Crysis2 is peer 2 peer = relying on someone elses connection to provide the multiplayer connection.

Dedicated servers = Crytek/EA provide servers which everyone connects to. This provides a level playing field for ALL and should reduce lag / ping times. Servers are basically just great big bad ass computers.

"Dedicated servers are the Future, Post human Video games will have dedicated servers"

With love from.

J. Hargreave.

as above, but with a bit more info.
Most console games( and a few pc ones) use peer 2 peer which means one of the people playing the game is also hosting, so his console is also running the game server for everyone that they are playing with, and it relies on sharing each players internet connection with the host players connection doing most of the work. so is hugly limited by slower internet connections which is why console games normally have less players per game, ie max of 16.

A dedicated server is an industrial computer and is normally in a server farm with immensely powerfull industrial broadband connections that can have hundreads of players connected at the same time. and its dedicated to just running the game server, not playing it. so you can have dozens or even hundreds of players on the same game with good pings and smooth gameplay,

Dedicated servers are far better, but obviously cost far more, and are normally rented for gaming.

I rent 5 dedicated servers for our gamecommunity which cost me about 250 quid every 3 or 4 months , but that includes voice servers and we can change what games we want to run in a few minutes.