Hitman: Contracts is a third-person stealth game. Players take the role of "47", a hitman who is unlucky enough to get shot, and falls to the floor dying. The whole game takes place in "flashbacks", where 47 is reminiscing about past missions, some of which were previously seen in Hitman: Codename 47, the first game from the Hitman series.
Gameplay in Hitman: Contracts is similar to the previous installments. Your job will be to complete several missions which involve assassinating targets all over the world. You can sneak around in disguise to avoid the suspicious guards, or you can instead open fire on everyone you see. When you complete your mission, you're given a rating - from "Mass Murderer" up to the coveted "Silent Assassin". If you manage to complete a mission with a "Silent Assassin" rating, you receive a reward: a special weapon (such as dual sawed-off shotguns), and you can try playing a previously completed mission using one of the special weapons.
A large majority of the levels in Hitman: Contracts are simply remakes of the levels from Hitman: Codename 47. Almost all of the major missions from the original game have been remade in Contracts, the only major levels that weren't remade were the Columbia mission where you assassinate Pablo Ochoa, and the deathmatch-style final confrontation in the Asylum (both of these levels were very action-oriented, and were probably deemed inappropriate given the Hitman series later focused on more crafty, less rambo-ish gameplay).