The name Thaylia means To Blossom Or Flourish and is of Greek origin. Thaylia is a name that's been used primarily by parents who are considering baby names for girls.
In Greek mythology, Thalia/Thaelia is the eight born of the nine muses, a goddess who presided over comedy and idyllic poetry. Thalia is the daughter of Zeus and Mnemosyne.
Possibly from the word root thallo meaning "to blossom."