Gamer points are what you get when you unlock an achievement but I don't know what you can do with them. Are they just to brag or can you cash them in or can you buy a game?
They don't "do" anything, they're just a counter for what you have achieved.
I.e., a gamer score of 10,000 is more impressive than a score of 5,000.
For the most part, the harder the achievement, or the longer it takes, the higher the achievement score. Finishing a level might be worth 10 Gamerscore, Finishing the campaign on Normal difficulty might be worth 50. Completing it on Hard might be worth 100.
However there are exceptions to this rule, like the "Go Get Some Sun" achievement in CoD: WaW, worth 0 Gamerscore, but requiring a lot of time and effort.
On the other hand, all 1000 Gamerscore from "Avatar: The last Airbender - The Burning Earth" can be easily unlocked in under 5 minutes.