The rhyl was a worm-like creature. Children from the Ba'ku planet, such as Artim, kept them as pets. (Star Trek: Insurrection)
Appendices
Background information
It is unknown if this "palm pet" was native to the planet, or if the Ba'ku brought them from their homeworld. The script of Insurrection described the animal as "a colorful cross between a caterpillar and a jellyfish". The name came from design notes, but was never mentioned in the film.
Like the Ba'ku hummingbird, the rhyl was a deceptively lifelike creature, yet a digital construct nonetheless, built at Blue Sky/VIFX, whose staffers incidentally, were the ones who utilized the moniker "palm pet" among themselves, managing to get the descriptive denominator elevated into the final script draft in scene 87. For further information on the CGI model of the rhyl, see: Rhyl model.
A licensed tie-in beanie toy of the Ba'ku rhyl was made by The Idea Company and sold, for a short time, at Star Trek: The Experience at the Las Vegas Hilton.
Apocrypha
According to the RPG sourcebook Creatures, the rhyl has the ability to use the metaphasic particles bombarding its planet to enter into "slow time". This causes the rhyl to suddenly disappear from view, enabling it to escape from predators.