Prometheus -- his Greek name means forethought -- was a Titan who stole fire from the Gods and gave it to humanity, initiating all the arts of human civilization but angering the Gods, especially Zeus. In various versions of the myth, Prometheus was also held to have been the creator of humankind, molding human beings from clay, and guarding humanity against the angry Gods. Another thread, and this one clearly represented in Percy Bysshe Shelley's drama, Prometheus Unbound, is that the Titans and Gods were equally matched in their internecine war until Prometheus struck a deal with Zeus to throw his power on the side of the Gods in return for a pledge that Zeus would free humankind from servitude. After Zeus won, he reneged on his promise and chained Prometheus, along with the other Titans, for perpetuity.
For his actions, however they are construed, Prometheus was severely punished by Zeus. In the version related by Aeschylus in Prometheus Bound, the most influential account from classical antiquity, Zeus chained Prometheus to Mount Caucasus and set upon him an eagle (in other versions a vulture) who each day ate away at his liver which would be regenerated by night.
Mary Shelley was well aware of these mythic archetypes. Growing up in the Godwin household, she would have known, and probably also have been educated upon, The Pantheon, or, Ancient History of the Gods of Greece and Rome (1806) by "Edward Baldwin," the pseudonym under which Godwin wrote books for children. This was a handbook on classical mythology with a section devoted to various versions of the Prometheus myth. She was also aware of the two main threads of the Prometheus legend, Prometheus as bearer of fire and as creator of humankind, since they are both registered in the early lines of Ovid's Metamorphoses, which her reading list notes her perusing in 1815.
Mary Shelley was not the first to invoke a "modern Prometheus." The Earl of Shaftesbury mentions Prometheus three times in The Moralists (1709) including a reference to "our modern PROMETHEUS's, the Mountebanks, who perform'd such Wonders of many kinds, here on our earthly Stages."