In the original comics, Beast Boy's powers are the result of a serum called "Sakutia", created by the evil scientist Doctor Niles Caulder, also known as The Chief. Caulder used Sakutia to give Garfield the ability to transform into animals as a way to cure him from a rare disease, "Sakutia fever". The serum worked and gave Garfield his shapeshifting powers.
In later comic book adaptations and animated series, Beast Boy's powers are sometimes explained as being a result of a rare genetic mutation or an encounter with an extraterrestrial entity. In the 2003 Teen Titans animated series, for example, Beast Boy's powers are portrayed as a natural ability that he developed during puberty.
Regardless of the origin of his powers, Beast Boy has the ability to transform into any animal he chooses, but he cannot maintain his animal forms for an extended period of time. As he gains more experience and control over his powers, he is able to stay transformed for longer periods.