Mother Brain is a fictional creature from the Metroid universe. She first appeared as the final boss of Metroid, the first game in the Metroid series. She is apparently the leader of the Space Pirates (Though officially it is unclear), and the archvillain Samus Aran must defeat. Originally, she was something of an organic computer for the planet Zebes. Mother Brain would control it's defenses, and possibly things like its atmosphere.
Mother Brain may or may not be the leader of the space pirates. Some official sources claim Ridley was always the leader, while other just as official sources claim it was always Mother Brain. The disparity and confusion can be attributed to different companies in control of telling the story (From creators of the official manga to the team behind Metroid Zero Mission to Retro Studios), who don't seem to be too worried about consistency.
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Mother Brain reappears in giant dinosaur form despite being defeated and ruined by Samus in Super Metroid. It is thanks to a baby Metroid sacrfices itself that Samus wins.