This video (8:16) shows a tourist displaying a ladder going into an underground shaft at the base of Sphinx.
Just wondering what is inside it and its purpose.
Probably sand and limestone and that's about it. The narrator in the video claims that there is a ladder, but it's conspicuously not visible in the shot. It almost seems like a reference to the crackpot theory of a Hall of Records or something along these lines.
An article in Smithsonian Magazine describes the extensive archeological work of Mark Lehner:
In 1977, [Lehner] joined Stanford Research Institute scientists using state-of-the-art remote-sensing equipment to analyze the bedrock under the Sphinx. They found only the cracks and fissures expected of ordinary limestone formations. Working closely with a young Egyptian archaeologist named Zahi Hawass, Lehner also explored and mapped a passage in the Sphinx’s rump, concluding that treasure hunters likely had dug it after the statue was built.
The small opening shown in the video you link, which a worker covered with what looks like a temporary hatch cover, is probably related to ground water erosion testing and abatement projects. The same article linked by Brian Z has the following section at the end (emphasis mine):
Today, the Sphinx is still eroding. Three years ago, Egyptian authorities learned that sewage dumped in a nearby canal was causing a rise in the local water table. Moisture was drawn up into the body of the Sphinx and large flakes of limestone were peeling off the statue.
Hawass arranged for workers to drill test holes in the bedrock around the Sphinx. They found the water table was only 15 feet beneath the statue. Pumps have been installed nearby to divert the groundwater. So far, so good. “Never say to anyone that we saved the Sphinx,” he says. “The Sphinx is the oldest patient in the world. All of us have to dedicate our lives to nursing the Sphinx all the time.”
Another article from 2007 discussing the issue can be read here Pyramids, Sphinx Threatened by Rising Groundwater.
A more recent article (2012) Egypt's Sphinx, Pyramids threatened by groundwater, hydrologists warn discusses some of the measures being taken.
Another You tube video with the sensantionalistic title "Caught Drilling Under the Sphinx...They Know What's Down There!" actually has footage beginning at time stamp 7:40 showing some workers drilling one of these test holes. Note the proximity to one of the reconstructed areas of the Sphinx, similar to the location shown in the OPs video.(Note at 8:08 in the OPs video the pipe-like fitting straight out from the mysterious opening).
A video about mysteries under the Sphinx gets many more hits,however, I think the 'mysterious' works under the Sphinx are very un-mysterious plumbing projects meant to monitor and protect it.
UPDATE: When I went back to YouTube, the video Drilling under the Sphinx (Featuring Dr Zahi Hawass and Dr Mark Lehner) was at the top of my recommended list. This short video (3:47) seems to be the source for the footage of the workers, and has Hawass and Lehner discussing the ground water testing/measurement project.