i think dedicated servers have been explained ok but a few good points have ben missed.
at the moment: to play a multiplayer game one of the players computers in the game has to basically "run" the game as a server as well as play the game.
This computer could have anything from a fast (T1+) connection down to a 56k modem. The faster the connection the "host" has, the faster the game will be for everyone else. Unless the host has a fast computer, everyone will be slowed down as their computer not only has to play the game (which slows down a lot of computers itself) but also run as the server. So basically, the slower the computer and connection, the worse it will be for everyone else. That 1 player also has a lot of power, if he wants to quit he will more than likely just exit and cut everyone off, end of game for everyone.
when we have dedicated servers: an isp or anyone with a really fast computer/connection can set up a machine to do nothing but host games, they won't have to be playing the game and configuring everything, they just basically run the dedicated server client and walk away.
When you play most multiplayer games, thats whats happening, everyone is connecting to a permanent dedicated server that isn't a player in the game.
If an ISP or whatever in your area sets up a permanent dedicated server on a decent connection, you won't have to use gamespy, OFP can just connect to that server and off you go, fast low ping game.
Dedicated servers are a MUST. They will help a lot for LAN games as well, install it on the worst machine there and off you go. Dedicated servers usually don't take a lot of CPU power as they are not actually playing the game, they are just keeping track of what everyone else is doing, where everyone is, who's shooting, who's hit, who's dead etc etc and relaying that information to each computer connected to it. ISP's that run game servers often have multiple dedicated servers running on 1 fast machine.
So basically, they will be something that ISP's, hopefully BI or anyone with a fast connection can set up to allow other people to have fast games.