Balancing corrects weight distribution around the wheel and tire assembly. Tiny weight differences become significant at speed, so a fitter spins the wheel on a machine and adds small weights until it runs true. The symptom of imbalance is vibration, usually through the steering at a particular speed.
Alignment sets the angles at which your wheels meet the road - camber, caster and toe. The symptoms of poor alignment are a car that pulls to one side, an off-centre steering wheel, or tires wearing on one edge.
Balancing happens every time a tire is fitted. Alignment is worth checking after hitting a significant pothole or kerb, when fitting new tires, or roughly once a year.
Both are quick jobs. You can book either online.