What does the number next to achievements mean?

Solution 1:

The number signifies the amount of "Achievement Points" the achievement is worth. The amount of points directly corresponds with the Achievement's difficulty.

As of right now I cannot find a way to see all achievement points accrued. I don't like the current achievement menu; it shows you your 6 most recently earned achievements but you have no way of reading a description for them unless you find them on the drop down list. I would say achievement points are mainly for personal satisfaction; think of them as a reward for doing certain things. Some people may not feel like they have 'completed' a game until all achievements are unlocked. They give players something to use as a goal.