What is CP? Why is it important?

Pokémon have a statistic called CP. What does it do, and why is it relevant?

Is it a substitute for the nonexistent levels and statistics, or is it something completely different?

Solution 1:

CP is an abbreviation for Combat Power. It is an aggregate statistic that represents how powerful any specific Pokemon is, based on their IVs (Stamina, Attack, and Defense) and their current Level.

It is a safe (general) assumption that a Pokemon with a higher CP will tend to fare better in battle than one with a lower CP. If two Pokemon of the same species, CP, IV, Level, and Moveset were to battle, the fight will likely result in a draw.

CP, however, is not a determination of who wins a battle. There are a number of extra factors that influence battles:

• Type Advantages
  Like all previous Pokemon games, type advantages between different Pokemon still take effect. For example, a Water Pokemon will have an advantage over a Fire Pokemon.
• Same Type Attack Bonus
  If a Pokemon has the same Type as the move being used, a Pokemon will gain a 25% Attack Boost.
• IVs
  Pokemon, like in the main series, have IVs on their core statistics. A high-Defense Pokemon may very well fare very well against a Pokemon with a higher CP, depending on the attacker's IVs.
• Speed
  Typically, a Trainer has an inherent edge against a Gym Pokemon because a Trainer can attack faster and with more ferocity.
• Dodging
  Trainers may "dodge" attacks from Gym Pokemon, with grants them a specific advantage that may turn the battle into their favor, regardless of IVs.

Two Pokemon with the same CP are not always equal -- they may have different levels and IVs, making them vastly different and useful (or useless) in different cases.

CP can be increased by powering up the Pokémon through the use of Candies, and through evolution. Note, however, that CP will not cause your Pokémon to evolve -- this must be separately triggered.

Pokemon CPs can range from a minimum of 10 to an upper limit determined by their IVs and a Pokemon's Level. A list of Max CPs are available here, for those who are interested.