Doomsday is a Team Fortress 2 map with the gamemode Special Delivery. Special Delivery is a mode similar to Capture the Flag, but there is only one neutral briefcase that can be picked up both the RED and BLU teams. Upon a team picking up the briefcase, the opposing team will be unable to pick up the briefcase until it has been dropped for 45 seconds and respawns as a neutral briefcase. A team wins by carrying the briefcase onto a loading platform, which will gradually rise until the platform reaches its peak.
On Doomsday, both teams attempt to deliver a package of Australium to Poopy Joe to use as fuel so he can fly a rocket into space. Both teams compete to deliver the Australium to the launch pad and stay there until they can insert the Australium into the rocket's tip. Once inserted, the rocket launches upwards, encounters a staggering failure in the engines after a short time in the air, and crash lands upon the enemy's base, destroying a laser relay (facing the rocket from the platform, the BLU base is to the right, and the RED base is to the left). Doomsday is created by Valve Software and was a part of the Pyromania update (day 1 of the update) on June 27th 2012.
You can find the Doomsday community strategy guide here