Natures decrease and increase a certain stat by 10%.
A Pokémon's Nature usually affects the growth rate of two of its stats, ultimately increasing one of its stats by 10% and decreasing another by 10%. Natures also determine the Pokémon's favorite flavor and its disliked flavor.
Which stat it increases and decreases depends on the nature.
A Pokémon's Characteristic is determined by the remainder of its highest IV divided by 5.
Characteristics determine what number of IVs a Pokemon can have in a certain stat.
For example: a Pokemon that "loves to eat" can have 0, 5, 10, 15, 20, 25 or 30 IVs in HP
IVs are one of the most important things in determining stats. From Generation 3 onward it uses this formula to calculate a Pokemon's HP stat and other stats.
Hope I helped!