The Tempest is one of Shakespeare's last plays, and one that seems to have no source material. This opens up the question: what is the inspiration for this play? Some would say there is no historical source material because the source of inspiration is Shakespeare himself.
Many people believe that Prospero is an autobiographical character. They have interpreted Prospero's speech in which he gives up his magic as Shakespeare's farewell to the theater. He says "our revels are now ended" and later asks for applause to "set him free." The main reason for people thinking this play is autobiographical comes from the character Prospero.
Prospero also makes mention of "the great globe itself," which potentially could be a reference to Shakespeare's Globe Theater. The island is bare, much like how stages at the time would often lack elaborate sets. The magic that occurs on the island could be an allegory for the idea of "magic" being created during a performance, as performances can transport audiences into stories.
At the end of the day, we don't really know for sure if The Tempest is autobiographical or not. This is just a reaction that some readers and Shakespeare scholars have.