Well, as Lovecraft liked to do, it's not laid out explicitly, but, here's how Wikipedia describes it:
As the two progress further into the city, they are ultimately drawn to a massive, ominous entrance which is the opening of a tunnel which they believe leads into the subterranean region described in the murals. Compulsively they are drawn in, finding further horrors: evidence of dead Elder Things caught in a brutal struggle and blind six-foot-tall penguins wandering around placidly. They are confronted with an immense, ululating horror in the form of a black, bubbling mass, which they identify as a Shoggoth. They escape with their lives using luck and diversion. On the plane high above the plateau, Danforth looks back and sees something that causes him to lose his sanity. He refuses to tell anyone (even Dyer) what he saw, though it is implied that it has something to do with what lies beyond the larger mountain range that even the Elder Things feared.
Professor Dyer concludes that the Elder Things and their civilization were destroyed by the Shoggoths they created and that this entity has sustained itself on the enormous penguins since eons past. He begs the planners of the next proposed Antarctic expedition to stay away from things that should not be loosed on this Earth.
You can read it free, btw, via WikiSource, as well as a few other places, as I believe it's entered the public domain..
Here's the text, though, with what IS available in the story about what he saw:
All that Danforth has ever hinted is that the final horror was a mirage. It was not, he declares, anything connected with the cubes and caves of those echoing, vaporous, wormily-honeycombed mountains of madness which we crossed; but a single fantastic, demoniac glimpse, among the churning zenith clouds, of what lay back of those other violet westward mountains which the Old Ones had shunned and feared. It is very probable that the thing was a sheer delusion born of the previous stresses we had passed through, and of the actual though unrecognized mirage of the dead transmontane city experienced near Lake's camp the day before; but it was so real to Danforth that he suffers from it still.
He has on rare occasions whispered disjointed and irresponsible things about "The black pit," "the carven rim," "the protoShoggoths," "the windowless solids with five dimensions," "the nameless cylinder," "the elder Pharos," "Yog-Sothoth," "the primal white jelly," "the color out of space," "the wings," "the eyes in darkness," "the moon-ladder," "the original, the eternal, the undying," and other bizarre conceptions; but when he is fully himself he repudiates all this and attributes it to his curious and macabre reading of earlier years.