Scenarios
Most war-games have scenarios, game variants players can select, that have differing victory conditions. Sometimes these conditions may be as simple as a time limit and a tally of kill points. He who kills the most wins. Most scenarios are more sophisticated, dictating deployment zones, turn limits, special conditions and so forth. The heart of most modern scenarios are objective markers.
Objectives
Objectives are token which one side or another must capture in order to win a scenario. Usually, they are slightly larger than a typical infantry base. They are also typically different than normal terrain -- no matter what awesome stuff players model on the base, it doesn't block line of sight or act as terrain. I've seen games use objectives in a number of different ways:
Sudden-Victory Objectives
If a player captures one of these objectives, then they win (usually at the start of the next turn). Flames of War uses sudden-victory objectives in all its main scenarios. The objectives are usually asymmetrical -- player A must capture player B's objectives. Player A must defend their own, but can't win just by holding it.
This system can produce any number of interesting scenarios. For example, the basic Flames of War "Free for All" scenario consists of two A objectives and two B objectives, on opposite sides of the table. Player A must capture the B objectives while defending his own A objectives. More complex variants of this set-up add reserves, ambushes, and so forth.
Sudden-victory objectives are particularly good for asymmetrical scenarios with an attacker and a defender. In many Flames of War scenarios, such as "Hold the Line" and its variants, the attacker must take objectives to win, but the defender has no corresponding objectives of his own. He must defend objectives for a number of turns.
Point-Based Objectives
In this variant, control of an objective generates points, and the points are needed to win. The current edition of Warhammer 40k's objectives do not trigger victory or defeat until a particular turn. At the end of the game (which is randomly determined), both players tally the number of points they have generated to see who has won.
Warhammer 40k's scenarios generate between two and five objectives, which players alternately deploy on the board. Normally, players end up with a board that looks like Flames of War's free-for-all, with two in each player's deployment zones. But it can also produce some strange set-ups. Sometimes one player will put all the objectives in their enemy's deployment zone, if they have a very aggressive army they don't want to split. Sometimes, there will be only two objectives -- a scenario my local group calls "roll dice and draw" because of the difficulty of capturing such a well-defended point. And sometimes an odd number of objectives will favor one player over another mercilessly.
The objectives need not always be worth the same number of points. In the I-95 gamer's "Domination" scenarios or Warhammer 40k's "The Scouring Scenario", each objective is worth a different number of point -- how many may not be revealed until it is captured.
In some scenarios, an objectives' points may contribute each turn to a tally. If a player reaches a certain tally, then they win. I-95's "Domination" scenario uses these mechanics. So too does Flames of War's multi-player Battalion-level scenario.
Oddball Objectives
Finally, there are funky objectives. Saga (which usually doesn't use objectives at all) has a cart scenario, in which one player must intercept and kill a moving cart. The cart is thus a kind of objective. Similarly, Warhammer 40k has a scenario where players fight over a moveable objective, like a free-flowing king of the hill.
Objectives can also combine with other types of victory points or conditions, such as points for killing enemies, time limits, and so forth.
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