In the games

Team Aqua appears only in the Hoenn-based games Pokémon Ruby, Sapphire, and Emerald, as well as their remakes Pokémon Omega Ruby and Alpha Sapphire, where they scheme to bring Kyogre out of its slumber.
Generally, Team Aqua Grunts have weaker Pokémon, with Zubat and Poochyena plentiful among them, however, they also use Pokémon of other types; typically they are Water types such as Carvanha (and Wailmer in Emerald). The team is headed by Archie and his two immediate subordinates Matt and Shelly.

In Sapphire
Though they are first encountered early in the game, their first major plot is to use the Meteorite to cease the eruption of Mt. Chimney, which would cause rainwater to fill the cooled-down crater. When this is thwarted by the player, they set themselves up in Lilycove City's cove, planning their next moves. Their final action in the storyline is to steal a submarine from Slateport harbor, which they use to travel to the Seafloor Cavern with the Red Orb, where Kyogre awaits. Kyogre, however, is not able to be controlled, and leaves for the Cave of Origin in Sootopolis City where it must be captured by the player or defeated.

In Ruby
Team Aqua is relegated to a supporting role in Ruby, with Team Magma instead performing the same actions (with different reasoning) and awakening Groudon instead.

In Emerald
Team Aqua's deeds are partly the same in Pokémon Emerald as they are in Sapphire, with them stealing the sub to obtain Kyogre. After awakening Kyogre and seeing Kyogre and Groudon clash together, both Team Magma's Maxie and Team Aqua's Archie realize what they've done has caused a terrible disaster, and make peace with one another after Groudon and Kyogre have been taken care of by Rayquaza.