The baby alien is an alien that lives in the fifth dimension.
Heinz Doofenshmirtz made an away-inator specially for monster trucks. Heinz Doofenshmirtz didn't know where the away-inator teleported the things until he and several evil investors were teleported to its dimension. Upon seeing Doofenshmirtz and the investors, the baby alien eats them all. It is unknown how Doofenshmirtz and the investors escaped back to their world. ("It's a Mud, Mud, Mud, Mud World").
Dr. Doofenshmirtz later uses the away-inator to teleport a biker who offered to give Doofenshmirtz's daughter, Vanessa, a ride. The biker was then smashed by the alien baby's toy hammer. ("Vanessassary Roughness").
The alien unintentionally comes to the first dimension when Perry the Platypus breaks the Accelerate-inator and sends the time stream several hours into reverse, ripping a hole in the time-space continuum. It destroys the inator before it was ever used. It is unknown what happened to the alien after that, though hopefully the paradox corrected itself ("She's the Mayor").
During the alien's first appearance it was yellow and smaller than Doofenshmirtz and the evil investors. In its later appearances, the alien is green and much bigger than Doofenshmirtz. This may be because the alien became somewhat older.