The terms come from The Forge.
The basic idea is that conflict resolution is much more abstract than task resolution.
In conflict resolution, the main concept is the intent, i.e. what the player wants to happen in the shared imagined universe, while the task is how he does it.
Then, if the player gets a success (using dices or whatever) the GM must fulfil the intent. Usually, the consequences of failure are also stated.
It is really more powerful than for example D&D 3.x Move Silently where you have to do a check every time you move your full round movement.
I could say more, but I would have to talk about a specific implementation, for example how Burning Wheel does it.
For example, you could have a player saying : I want to sneak in the house and grab the X I need without being noticed. It could be all resolved doing a "Sneak" skill test, where failure is for example a witness that may come back at him later (but he gets the X anyway).
With such a system, fudging is a thing of the past.