Higher CP values mean the Pokémon will be stronger and will hit harder.
When capturing Pokémon, CP is either directly displayed, or three questions marks may show (???). CP and the difficulty of catching a Pokémon is not always correlated, as it is possible for a low CP Pokémon to have a yellow ring when capturing.
The higher the level a trainer is, the higher the CP of a Pokémon can be. Wild Pokémon caught will also have higher CP as the trainer levels up. As the trainer levels up, the maximum potential CP of a Pokémon will rise. Once the trainer has reached level 30, the CP ceiling for wild Pokémon is capped; hence a maxed-out Pokémon will not get any stronger. A similar cap for Pokémon hatched from eggs is reached at 20.
Check the Individual Values page for the formula used to calculate a Pokémon's CP.