The crystal skulls in the film are the skulls of inter-dimensional beings that came to Earth to learn about its culture and peoples. There were thirteen such beings, which were worshipped as gods by the ancient Mayans, centered in the mythical city of El Dorado (aka, the City of Gold). Years ago, one of the skulls was taken from the city by an explorer, only to be discovered by Professor Oxley (John Hurt) during the time period of the film. A team of KGB agents, led by Irina Spalko (Cate Blanchett), are trying to take the skull back to its original source in the ancient city. The skull, it is learned, isn't inactive, and can create psychic connections to certain people who stare into its eyes. Indiana Jones (Harrison Ford), upon staring into its eyes, learns that he must return it to the ancient city. Indy and crew return the skull, only to discover the skeletons of the twelve other beings and one headless skeleton. Upon being placed upon the spine of its rightful owner, the thirteen skeletons merge together into a single entity. Believers in the crystal skulls attribute all sorts of abilities to them, ranging from the skulls being psychic amplifiers to tools of death to repositories of ancient knowledge. See more here. Even though this doesn't seem to be an established lore or myth-type artifact, such as the Ark of the Covenant or the Holy Grail, there has been literature written on the subject and actual Mayan/Aztec artifacts of this nature found. This also explains why Aztec/Mayan pyramids have been placed at Indiana Jones fan conventions, Comic-Con, etc.
Co-producer George Lucas admitted in an MTV video clip that he has been obsessed with these antique crystal skulls ever since he began doing research for The Young Indiana Jones Chronicles TV-series that premiered in 1992. "We did The Young Indiana Jones Chronicles," he said, "and in the process of that, one of the scripts we were working on was about a crystal skull. I became fascinated with it there." Lucas also revealed on the red carpet for the American Film Institute's 40th anniversary at the ArcLight, "We've been through lots of different versions the last 14 years, with five different writers. There's just a lot of aspects that seem to fit into our kind of a movie...I think this is actually better, it's up there with the Ark of the Covenant," he declared of the fourth film's "McGuffin" (a term coined by Alfred Hitchcock to describe an object which drives a film's plot). "Sankara Stones and the Holy Grail were a little tough, but I think this time we've really got a great one." Lucas emphasized that The Crystal Skull is shaping up to be the best Indy flick since the first one, even going so far as to call it tonally most like Radiers of the Lost Ark. Co-producer Frank Marshall mentioned this concerning the Crystal Skulls: "The theory is they are shaped by higher powers or alien powers or came from another world, or an ancient Mayan civilization had the powers."
For more information about the crystal skulls, check out an interesting documentary on the subject, which also mentions Atlantis here and here. An amateur video of the Crystal Skull ride in Disney Tokyo can be seen here. LEGO has decided to represent them in this manner here.