You might enjoy Lindybeiges videos as an explanation to this question. It has lot's of practical info on warfare. I don't know how to make this into a URL link so you will have to do the good old copy paste method.

http://www.youtube.com/watch?v=boioSxBIkfk http://www.youtube.com/watch?v=hqtp08ZSAYE

I can give a few reasons why axes were practical:

1. Lots of people had them, axes were used in many professions so when you had to round up a bunch of men you would be thrilled to hear that they already had a good axe and knew how to swing it. Weapons from this period in time often had their origins in agriculture.
2. They were cheap. Just have a look at a simple axe, it has quite a large head on it but besides that it's quite easy to produce. Especially when compared to a sword.
3. Force. Like the hammer the Axe was a weapon that could transfer a lot of force to the target. It has a heavy head so that you can easily swing it, multiplying the speed with which you swing and land it on a poor man's head. Just like with a hammer you wouldn't necessarily have to penetrate the enemies armour to cause them great injury. Compare this to a spear, sure, you can give a good thrust with a spear but it would be difficult to find enough room to swing a spear. A sword might be more suitable for swinging but swords are relatively vulnerable and tend to break. I hope my post made some sense.