Support Pokémon are the Pokémon that are on the player's team while playing a stage. The player can choose up to four of the Pokémon that they have caught to bring to battle on a stage, unless the stage is a 3-Pokémon Stage, in which case the player can only bring three.
The first slot is usually reserved for a Mega Evolving Pokémon, since it is required for Mega Evolution for the Pokémon to be in the first slot (in addition to possessing the respective Mega Stone). The other three slots can be any caught Pokémon, but they can't Mega Evolve.
If a slot is empty (which happens by dragging the Pokémon icon out of its slot) when the player starts a stage, the stage will automatically fill in the slot with its Default Pokémon, whether the player has caught them or not.
The player may use the Optimize button to have the game automatically choose an optimized team for them.
Some stages come with 5 Pokémon: four as Support Pokémon, and one as a Non-Support Pokémon.