From Bulbapedia, the community-driven Pokémon encyclopedia.
A full battle (Japanese: フルバトル full battle), also known as a six-on-six battle, is a Pokémon battle in which both trainers use a full party of six Pokémon. The first trainer to completely knock out all of the opposing trainer's Pokémon wins the battle.
These battles are rare, both in the anime and the games. Usually trainers will either have or useless than the full six.
In the anime, most trainers declare a specific number of Pokémon to be used in a battle. This number is very rarely the full six. The most notable trainer to do so is Drake, the final leader in the Orange League. Battles in the final rounds of each region's League Conference are usually full battles as well.
Unlike the anime, the games allow two trainers to use different numbers of Pokémon. While the player will more often than not have six Pokémon with them at a time, many NPCs they face, including Gym Leaders and members of the Elite Four, will not.