You have several different compounds to choose from but during the race they will be called the Prime tire and the Option tire.
Prime tires are harder = last longer but less grip
Option tires are softer = wear quickly but lots of grip
Regulations say you have to use both sets, unless it rains, then the requirement is waived. Ideally, you would start on one set and then move to another during the course of the race, but because of the way the tires wear, most drivers will have to stop several times. With mandatory tire changes you have pit stops become part of the strategy, which can help or hinder a driver and also shuffle the order on the track during the race.
Also, you can't mix and match tires. You take all four Options or Primes, but not a mix of two each.
Pirelli makes super-soft, soft, medium, and hard tires. Only two of the four types are allocated each race depending on the track.