No one knows the answer to this question, although there have been many guesses from expert archeologists. One of the most interesting things that I have seen is that they believe that the outside of the Sphinx was weathered by water for many years. This is pretty impossible in what is now the Sahara Desert; however, it may have been possible if the Sphinx is a lot older than has been thought previously, and was possibly either under water, or in an area that flooded a lot. Another interesting speculation is about the choice of a lion's body for the Sphinx, and they believe that it could represent that the astrological age of Leo was coming into being (like we are now in the age of Aquarius). The Sphinx faces exactly towards where the constellation Leo would have been seen in the sky at the time , making the connection even more likely.
I've read that one of the guys that first speculated on the weathering of the Sphinx puts the date about 12,000 years ago. This is also supposedly a time around some great cataclysm that wiped out older civilizations. It sounds possible, although I'm not sure what the cataclysm was or where the evidence can be found. If there were some great cataclysm, that would explain a lot.
I watched a very interesting documentary about the head of the Sphinx, it stated that they felt that one of the Egyptian pharaohs had change the head, thats why it is so small to the proportion of the body. The thought was (If I recall right) That it might have been a bull (Taurus) or a lion. They did talk about the water marks, or the thought that the erosion on the body was caused by water, and in fact stated they felt a pool sat in front of the feet of the Sphinx. It appears they found the equivalent of fencing or better described as a stone wall that surrounds the a large portion of the Sphinx. I had read that they discovered via sonar that there is a void under the one foot (left I think) that maybe a chamber and there are scientists trying to get permission to excavate. I think I saw the documentary on the Smithsonian channel via Roku, it was very interesting. You can read about this on the Smithsonian site and they do have a short video, but I am thinking if you click around you usually can find the full documentaries they stream for Roku someplace for free on either the website or elsewhere on the web. The Smithsonian Channel has some really neat stuff if you like to watch factual TV. I think you can watch these online just by double clicking. I am not sure though. The shows change every few months. Some really cool topics sometimes are available, so it is worth a book mark.
"Most Egyptologists think that the Sphinx was built during the 4th Dynasty (around 2,500 BC) by the pharaoh Khafre. Unfortunately archaeologists can't carbon date stone, so we have to rely on other methods to approximately date the Sphinx. Although, theories have been presented opposing the commonly held theory by mainstream Egyptologists. This concerns the water erosion and the weathering of the Sphinx which don't match up with the date of 2,500 BC. The Orion Theory pushes the construction date all the way back to ~10,000 BC." ~According to yahoo, that's what I found.
I love things like this. I have seen other weird things about the Egyptian structures as well. It is pretty fascinating how all of these structures seem to align with certain star constellations or other astronomical anomalies so perfectly. It makes you wonder if they were capable of so much more than we know about today.