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.
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.
The comet has only appeared in "The Comet," however the Catalyst Comet has been mentioned in many episodes before this one and they appear to be one and the same.