Balance, alignment and rotation are generally the tire jobs that you can't do yourself. Anyone can check tire pressure, change a flat, and notice low tread, but unless you have training as a mechanic, do not work on your tires' balance, alignment or rotation.
Balance: Your tires should have equal weight on all sections, and if they don't, you'll notice your car vibrating, particularly at higher speeds. Poor balance will wear on your car's suspension, make your car more difficult to drive, and wear out your tires quickly. Mechanics will rebalance your tires when they mount and rotate them, but you can also bring in your car specifically for that purpose.
Alignment: Technically, it's your wheels that are aligned, not the tires, but poor alignment will cause uneven tread wear on your tires. A properly aligned car has appropriately functioning suspension and steering, and it shows in the straight running of your tires. You can check your car's alignment on a long, straight road with no traffic. Pull your hands off the steering wheel and see if your car veers to one side or the other; if it does, you need to have your car's alignment repaired.
Rotation: Tire rotation occurs when the mechanic switches your tires to different wheels. You should have your tires rotated every six to eight thousand miles (do it every other time you have your oil changed) because, like balance and alignment, rotation will help ensure even wear on your tires.