Purple Comet is the Catalyst Comet that Orgalorg tried to absorb power from. The comet was saved from Orgalorg's grasp by Finn, and was able to reveal its true form. The comet gave Finn the option to either stay on Earth, or go off and possibly become a god. Finn denied this request, and Martin ended up accepting this favor instead. Once the comet breaks apart and takes a purple orb form with three wide eyes, it reveals that they have known Finn even though they have not actually met outside of his human form. Once said comet reveals this information, the sound of a vault door opening can be heard as Finn puts his hands to his forehead, which is possibly refering to the fact that Finn sometimes seals bad memories or visions within a section of his subconsious he calls "The Vault" (Finn does this in the episode The Creeps when he sees the ghost of Shoko, one of his past incarnations, after escaping the haunted mansion on lady rainicorn's back, after looking at his vision, Finn says "That one's going in the vault, aaand it's gone")
The Purple Comet, having been the Catalyst Comet, was swallowed by Orgalorg in his attempt to take its power and knowledge. Soon after, Finn uses his thorn to cut Orgalorg so that the comet (or perhaps its energy) is released to form a purple spherical object with ribbon-like shapes cut out of it and three visible eyes.
The comet claims to have "been around forever" and "experienced so much impossible junk" and that it has "embodied all that is good and evil," suggesting that it is possibly omnipresent or used to be part of everything or everyone.