This one's a pretty simple mechanism that has been incorporated into a few games over the years.
The basic idea is that characters should be given some kind of currency to put a bit of extra effort into a task. This means that players get the opportunity to show the things that their character really cares about, and really wants to succeed (even if their skills wouldn't normally allow such a success).
In the Storytell(er/ing) System from White Wolf, this is reflected through Willpower points. Everyone gets 1 to 10 of these (typically averaging around 5 - 6, while most regular humans have 2 - 3). The system works off multiple degrees of success, and if a character really wants something to succeed, they spend a willpower point to improve their degree of success by 1. Each character and each NPC has their own pool of willpower points that may be used in this manner to adjust the storyline to their advantage.
In the d20 modern system, players and GM are assigned action dice. These may be rolled and added to existing die rolls in the hope to push a task over a difficulty threshold value. Players start with a fixed number of dice, and the GM has a fixed initial number of dice calculated by the number of players and other factors. The players are encouraged to use these dice, and the GM is encouraged to use his; dice are distributed back to the players and GM after appropriately dramatic points in the game.
The system used in the Serenity Roleplaying Game, offer plot points. These are accrued for relevant deeds in the game, such as "role playing, good ideas, and succeeding in goals" (a direct quote from the book). Once earned, they may be spent to increase the types of dice used in an action before the die is rolled, or allow additional dice to be rolled. That system got pretty complicated with who rolls what? how many dice get rolled? When do you add dice or straight modifiers? Which dice got modified...but anyway, that's getting off topic. Plot points could also be converted to XP at the end of a session (in fact any plot points above 6 were automatically forced to become XP).
It's been a long time, but I vaguely remember the Karma point system of Shadowrun having a similar idea behind it. A player could spend a point from their current karma pool to gain an immediate benefit when performing a task, or they could save these points up for permanent purchases to improve their character.
The whole idea seems to have been an early attempt to put a bit more narrative control back into the hands of the players. This could have been simple illusionism or it could have been used to truly allow a stories destiny to move according to communal whim, it all really depended on the GM.
Still, it's a useful idea that has seen a lot more use in many recent games. Perhaps a good GM would take note of when their players are choosing to spend these points to improve their chances of success. If the expenditure tends to happen during social scenes, then it becomes obvious that the players view the social scenes as more important to the game.
Does this mean that they want more social scenes? Does it mean that the GM is placing too much emphasis on social scenes, and the combat oriented characters feel that the only way to survive such a scene is buy spending their valuable fate points?
Food for thought...