After logging into Pokemon GO and setting up your character, you'll soon find that each Pokémon in your inventory sits under "CP" and a number. Essentially, CP is Combat Points and it allows your Pokémon to deal more damage, the higher the CP rating.
Related: Pokemon GO Guide Hub
As you level up your trainer, you'll come across Pokémon with a higher level – thus more base CP.
Why is CP important? Well, when you take your Pokémon into a gym, its CP will determine how much damage your Pokémon does. The more CP your Pokémon has, the more damage that will be inflicted on your opponent.
Looking past the damage portion, you'll see that each Pokémon has a crescent over them (when you select the Pokémon and bring up its status screen). This crescent is a visual representation of the Pokémon's level, which can be increased through Candy.
As the Pokémon gains levels or evolves, its CP will go up.
Using Star Dust in battle will increase your Pokémon's CP and HP (health points).