I believe the points are commonly referred to as miles because you could accrue one point for each mile that you flew with an airline. Now the airlines are moving toward crediting points for the amount of money that you spend on tickets. Accumulating and redeeming these points can be a complicated "hobby."
I really couldn't begin to explain all the ins and outs of frequent flier miles, points, kilometers, credit cards, bonuses, transfers and so on in one post, but I can give you a link to a blog written by a very savvy travel guru, Gary Leff. He puts out a lot of good information and it will take patience to wade through it all. If you are willing to spend the time and effort to try to understand it all, you would be surprised how rewarding this "hobby" can be.
View From The Wing