Azurill is the child of Tracey's Marill, though it is unknown which Pokémon was the other parent. Misty mentions that Tracey gave it to her when it was just an Egg.
Azurill was seen briefly from The Scheme Team to A Real Cleffa-Hanger. In the former episode, it was only seen at the very end, where it was shown that Misty carries it in her arms in the same way as she carried her Togepi.
In the next episode, it battled Team Rocket along with other Marill. It interacts very well with other Pokémon, most notably a wildCleffa.
As a baby Pokémon, Azurill is very playful, as seen when it was playing with a wildCleffa, using the ball on the end of its tail to entertain the Star Shape Pokémon. It is also very sociable, helpful, and friendly towards other Pokémon, as seen when it healed Pikachu from his injuries by using Refresh.