The RED team stands for Reliable Excavation Demolition. The RED team has the advantage because in all of the Meet the characters name(soldier, scout, engineer, pyro, demoman, heavy, sniper, medic, spy) they are always portraid as being on the RED team. They always win in the trailers. Many TF2 players beleive that Steam gives the RED team advantages. Like getting more powerful weapons, or getting more crits.
The BLU team(yes, that is how it's spelled in the game) stands for Builders League United. The BLU team is always getting killed and losing in the TF2 trailers. TF2 players beleive that Steam gives the BLU team more underpowered weapons, and they don't get as many random crits.