Characteristics

Pokémon characteristics are a feature that got introduced in Generation 4. It is a description that indicates a Pokémon's highest (therefore best possible) individual value (IV) and usually is found on the Pokémon's profile screen. However, having a specific favorable characteristic on a Pokémon does not mean that it is viable for competitive play or end-game content such as the battle tower.

You should note that before Generation 6 (meaning in Gen 4 and 5 games), the Characteristics' descriptions 'Takes plenty of siestas' and 'Nods of a lot' were mistranslated as 'Often dozes off' and 'Often scatters things' respectively.

As aforementioned, having a specific favorable characteristic on your Pokémon does not guarantee that it will be viable for use on your journey. If you are playing Pokémon to capture them all and be the very best, Characteristics will only ever come into play when preparing for end-game content such as the Battle Tower, Battle Frontier, or similar post-game content. However, if you consider tackling said contents or even consider entering competitive play, characteristics become a determining factor on which you can judge a Pokémon's potential.

For reference, a Pokémon's Characteristic is determined by the remainder of its highest IV stat divided by 5. This value now determines how good or bad the general IVs of said Pokémon is going to be as they can never be higher than that value. Based on this information, let us assume that a defensive Pokémon with a "Sturdy body" Characteristic can end up with a 5 in Defense, making its overall IV allocation pretty bad as none can be greater than 5. Now compare that to a Pokémon with the same Characteristic having 30 points in Defense (its maximum IV value while having "Sturdy body"). This stat difference creates a much better IV allocation in general, therefore making the Pokémon in question much better overall when raised to the maximum level.