TvT refers to the Team vs. Team battles, in battlegrounds.
Players are assigned into two teams - the Saliko Fighters (with a red tabard), and the Ashaya Defenders (with a blue tabard). Any players on the same team as you are friendly - they will not be harmed by area spells that you cast, or receive debuffs from abilities such as Growl. Similarly, players on the other team are hostile to you, so they will not benefit from area healing spells such as Healing Springs.