What happened to humanity in "There Will Come Soft Rains"?

This question is not clearly answered in the story, but we can draw some conclusions based on Ray Bradbury's other works and the time of his writing.

Ray Bradbury was writing mostly during the 1950s.  This was a time of social optimism.  World War II was over, and compared to the 1940s, people were feeling very successful.  Unemployment was low and science was coming up with new discoveries and inventions at an alarming rate.  More...

This question is not clearly answered in the story, but we can draw some conclusions based on Ray Bradbury's other works and the time of his writing.

Ray Bradbury was writing mostly during the 1950s.  This was a time of social optimism.  World War II was over, and compared to the 1940s, people were feeling very successful.  Unemployment was low and science was coming up with new discoveries and inventions at an alarming rate.  More and more people were able to enjoy certain technologies in the home -- automatic dishwashers, vacuum cleaners, and similar items gave rise to the impression that science would make our lives very leisure-filled.  In the realm of science fiction, writers like Bradbury were exploring what would happen if technology continued advancing at such a rate. Perhaps humanity might no longer be needed.  We see this in "There Will Come Soft Rains" as the house seems to go through a very ordinary day, completely on its own, cooking meals, setting up a card game, preparing the nursery for sleep, etc. 

However, the 1950s were also the beginning of the Cold War, and along with the optimism noted above there was an underlying dread of the potential for nuclear war.  This, too, gave science fiction writers a fertile field for exploration:  What would the world be like if the Americans and Russians did set off nuclear bombs?  Would we destroy ourselves completely?

This seems to be the result in "There Will Come Soft Rains."  Though it isn't directly stated, this would be a plausible conclusion for the absence of any people.  Technology has advanced to the point that we see in the house, but the Cold War advanced also, and humanity has destroyed itself.  Only the technology remains.

However, then we see nature seem to survive over technology, as a random tree branch falls into the house and ignites an accidental fire.  The house tries to put out the fire, but the fire continues, and in the end destroys the entire house.  Nature overcomes technology.