What is a sphinx? What was its purpose?

The original purpose of the Sphinx is unknown. It may have been built to symbolically guard over the Giza plateau, and it may have been a portrait of Pharaoh Khafre. It's face seems to bear a resemblance to Khafre's, and the royal headdress that it wears is particular to pharaohs.

The purpose of the Sphinx was to guard the pyramids and crush the Pharaohs enemies that try to rob his tomb. It also means the wisdom and strength. that's what I would have thought it was without reading it.