Characteristics

In Diamond & Pearl, and likely subsequent games, there is a little note in the status screen which describes the Pokémon. This is derived from its stats, specifically its Individual Values

The note seen on screen will post your Pokémon's highest IV. However, it is a bit more complicated than that as each saying corresponds to multiple IVs. To completely confirm, you should still use an IV Calculator.

The characteristics are for all stats and can easily on first glance help you choose what to aim your Pokémon for being in battle such as more defensive or more offensive. Below is a list of all the Characterstics and the IVs to which they correspond