After Biff Jr. stole an arrowhead from Verne he'd been planning to bring to show and tell, Verne convinced Marty to drive him back to the prehistoric era, as he was forbidden from taking the DeLorean time machine himself. He eventually returned with a dinosaur egg, not considering the dangers of it hatching in the 20th century until too late.
Verne was barely able to hide the newly hatched baby dinosaur from his mother and was able to keep his father from noticing the temporal displaced beast when Jules helped him disguise it as their new friend "Elroy." Verne named the dinosaur "Tiny;" an ironic name choice as it was already growing at a rapid pace. Jules theorized that a biochemical reaction had resulted from Tiny's exposure to the present day atmosphere, causing the accelerated growth.
Tiny managed to escape the brothers' watch as the two discussed the ethics of keeping him in 20th century Hill Valley. He was subsequently spotted by Biff Tannen and his son who captured him and sold him to Mr. Wisdom for $50,000. Verne admitted what he'd done to his father in order to gain his help in finding Tiny, so Doc and Clara decided to go easy on their son because of his honesty. The Brown family, along with Marty, soon after caught sight of Tiny on Mr. Wisdom's TV show where the star announced his plans to dissect the dinosaur and sell him to multiple universities for research.
The family eventually managed to infiltrate the television studio and escape with Tiny, replacing him with a decoy worn by Marty and Jules. Having been successfully rescued from harm, Tiny was then boarded onto a railcar on the Jules Verne Train to be taken home when he spat out one of his baby teeth. Verne keeps the tooth, which Mrs. Brown says can be used for show and tell as it is an artifact that will not arouse suspicion.