The Stork is a secondary character who appears in Super Mario World 2: Yoshi's Island and Yoshi Touch & Go. His job is to deliver babies to their parents (which is based on the tale that the stork delivers babies).
One early morning when delivering the Mario Bros., Kamek came and snatched one of the babies and kidnapped the Stork. He holds the Stork and Baby Luigi as prisoners. This leads to the main plot where the Yoshis decide to reunite Baby Mario with his brother using the Stork's map to guide them. After a long and dangerous journey, the Yoshis finally come and rescue the Stork and Baby Luigi. The twins are reunited and the stork flies away into the night. The Stork is seen flying past clouds and mountains til it finally arrives at the village were Mario and Luigi's parents live. He leaves them at their door before flying off again to continue his work.
In Yoshi Touch & Go, when a challenge is complete the Stork will swoop down and take Baby Mario.
In Yoshi's New Island, the Stork reappears carrying Baby Mario and Luigi to their parents, however it turns out the Stork got mixed up and gave the babies to the wrong parents. Hastily, the Stork takes to the skies to deliver the two dynamos to the rightful parents however, in mid-flight Kamek and his Toadies ambush him making him drop Baby Mario onto the island and allowing Kamek to take Baby Luigi again.