Sounds like flat spots, if you bought road hazard protection you will be able to get new tires for around 30 bucks each(cost of the new roadhazard plus mounting)
The tires would go out of balance if the tire had been worn down it one spot. This would make the tire heavier on one side, thus throwing the balance off.
Get 2 new front tires, hopefully you bought the roadhazard protection.
And to answer your ? in the tite. balancing involves mounting the tire/rim onto a machine that spins the wheel and detects where the balance is off on the wheel. It will tell you where to mount wheel weights to the rim, to counter balance it.
An alignment involves placing the car on a rack and attaching "heads" to the rims. Like in this picture.
Here this link explains it pretty well
http://www.familycar.com/CarCare/AlignmentBalance.htm