The straightforward answer to your question is: something, but not enough to be absolutely certain of its origins or purpose. As I pointed out in an earlier answer devoted to the famous White Horse of Uffington, records of English chalk figures that antedate the late 1600s are extremely rare, and sadly the Cerne Abbas giant is not recorded before 1694.

For the most part, archaeologists and historians tend to believe this suggests the figure most likely has its origins in the seventeenth century. Ronald Hutton, a Bristol University professor who's a noted authority on folklore and paganism, puts the case in favour of a relatively modern origin by pointing out that we have several surveys of the Cerne Abbas area that date to before the 1690s, all of which conspicuously fail to mention the existence of the giant. Archaeologists who have investigated the figure also point out that it has changed shape significantly since it was first carved. Its erect phallus has been significantly lengthened (the original figure, it's suggested, had a smaller phallus and a separate belly-button; the current image combines those two features in one, to startling effect) and it at one time seems to have held a cloak over one arm.

The leading theory that seeks to explain an early modern origin for the figure suggests it was carved on the instructions of a Civil Wars era parliamentarian leader, Denzil Holles, who owned the land on which the figure is carved between 1642 and 1666. Although Holles was one of the five Members of Parliament whose attempted arrest, by Charles I in 1642, helped spark the wars, he was no enthusiast for Oliver Cromwell and the military machine that Cromwell created in order to end the conflicts. The archaeologist Joseph Bettey pointed out that Cromwell's followers and propagandists often depicted him as a "modern Hercules", and argue that the Cerne Abbas figure is intended as a ribald commentary on Cromwell-as-Hercules. In this version of events, the now-vanished cloak was intended to remind viewers of the legend of Hercules's slaying of the Nemean lion (whose skin he thereafter wore), and so helped to define the image, for contemporaries, as Cromwell. A commission of enquiry which sat in 1774 was told by villagers that the figure was "a modern thing" that had been cut on Holles' orders.

Those who favour the idea that the figure is much more ancient than this point to a physical feature beneath its outstretched left hand and suggest it may once have delineated a severed head. Seen from this perspective, the figure may have been made by the local Celts, for whom the head was a significant religious object.

Sources

Joseph Bettey, 'The Cerne Abbas giant: the documentary evidence,' Antiquity 60 (1981)

Timothy Darvill, Katherine Barker, Barbara Bender & Ronald Hutton, The Cerne Giant: An Antiquity on Trial (1999)