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 (???) if its CP is higher than any on your roster. CP and the difficulty of catching a Pokémon is usually correlated, although this also depends on the species in question.
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. 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.
The arc above a Pokémon on its page indicates how high its CP is relative to its CP potential with a dot. A Pokémon at level 1 (10 CP) would be all the way to the left, a Pokémon at the maximum level at your trainer level would be all the way to the right. This is not to scale however, as from a perspective of a level 30 player, a level 10 Pokémon would have the dot roughly in the middle.