Basically, it's a trade-off between hammers now and hammers later. If you take the 'hammers-now' track, you can cut maybe 5+ turns off the production of a settler, granary, or some other type of building. By getting that settler or whatever built faster, your empire improves more rapidly. As a general rule, I try not to chop forests unless there are some other tiles in the city radius with decent hammer production, i.e. hills or a resource like horses. If, on the other hand, the city is maybe size 3, has hills, and 6 forests, I'll start sharpening the axes. Also, I usually chop forest/hills very quickly since I know I can recover the lost hammer and 1 extra by building a mine.