Individual Values, or IVs, are per stat values from 0 to 31, set when a Pokémon is generated, that act like its genes. A Pokémon with a 31 IV in a stat finishes 31 points ahead of an identical one with a 0 IV at level 100.
In Generations I and II the equivalent values, called determinant values, ran from 0 to 15 and only four were stored, with HP derived from the others. Generation III rebuilt the system into the modern one: six separate IVs, one each for HP, Attack, Defense, Special Attack, Special Defense, and Speed, each from 0 to 31. Two otherwise identical Alakazam can differ by up to 31 points in every stat purely because of these numbers.
IVs are fixed on encounter, capture, or hatching, and for most of the series you could not change them. Breeding became the main tool for controlling them, because parents pass several IVs down, and holding a Destiny Knot from Generation VI onward passes five of the parents' twelve IVs to the egg. Later games added judges that grade IVs in plain language and Hyper Training, introduced in Generation VII, which raises a stat to its 31 IV value for battle without changing the underlying IV.
For a story run, IVs barely matter. For competitive play they decide Speed ties and survival by a point or two, which is why players breed for five or six perfect IVs and sometimes deliberately want a 0, such as a slow Trick Room attacker.
In play"Her Dragapult has a perfect 31 Speed IV, so it moves before mine every time."