The most widely used strategy in chess, is the strategy of the material advantage.
Most of the chess players know that the material plus of a meagre pawn may already win the game.
With this in mind, a lot of players try to win material during the game. This way they ensure a strategically won game.
Once the material is won, the strategy often changes.
The player with the material advantage now has a new threat. He threatens to trade all of the pieces and pawns and convert the resulting ending into a win.
Not all endgames with extra material will win though. The next position shows a two knight advantage. Nevertheless it's still a draw.
There's something else to watch out for while winning material.
You don't want your position to become lost while you're grabbing a pawn or so. You'll have to watch out for mating attacks and other positional problems.
Garry Kasparov, a former world champion, often sacrificed a pawn to get a winning position. This strategy even succeeded against high-level grandmasters.
So a material advantage may be important, but it's not the only thing to fight for.