Tank Superiority is a new gamemode available in the Armoured Kill DLC. It's a team based game, and the main goal is to capture and hold a flag for as long as possible. It is recommended that your team has a good balance of tanks and infantry units.
It is best to just play a few games until your team wins, and as for tips, remember to play the objective. Destroy the enemy tanks by using the Engineer class explosives, C4 or Laser Designator (Recon Kit). If in a tank, try to focus on enemy tanks and capturing the flag, and then pulling back and defending it.