Objective based play is one of two main multiplayer gameplay concepts, the other being deathmatch. The main difference between the two is that objective games have a specific method and set goals to win, you the player has to go acomplish a specific task in order to win the game. Whereas, in a deathmatch game the player has to eliminate the other team don't care how just do it. Instead of kills points usually determine who wins the overall game, often each game is divided up into multiple rounds.
Perhaps the first famous, and definatly the most iconic objective game type. CTF, has it is commonly abreviated, involves not necessarily flags but some object that one or both teams have possesion of that the other team has to steal and bring to a predetermined location. Other rules may vary from game to game, but that is the basic framework.
A very popular game time, in which the assaulting team has to take something, usually a bomb, to a predefined area or object in control of the defending team, and plant there, the defending team attempts to stop them. if they plant it the defending team usually has a chance to disarm the device.
Another famous objective variant, in King of the Hill the players attempt to take a marked off area the longer any one team holds the area the more points they get. There are three main variants of this game type King of The Hill (just one big hill in the middle), Multiple Hill (a variant in which there is more than one control point), and Movable Hill (A variant in which the hill locations shift).