Earth had become uninhabitable due to famine, with some blight slowly killing off various types of crops. The initially presented solution is that, once the Endurance finds an inhabitable world, humanity will exodus en masse to their new home. On his death bed, however, Michael Caine's Dr. Brand reveals that this was all a front; humanity may survive, but those on Earth are stuck their, doomed to extinction. This all changes when Murphy realises the second hand of her watch is actually her father sending a message to her from the singularity, providing her the solution to the problem Dr. Brand couldn't see. We don't see any of Earth after Murph's Eureka moment, but from where Cooper finds himself after his singularity experience we can piece it together. Essentially it's deserted, a la Wall-E. Without any planetary goal, the humans set-up their own space colonies. These are on an unknown number of space stations in our own Solar System, with the living quarters designed to look just like our own home world, complete with artificial sun. They're near Saturn for close proximity to the wormhole, allowing for exploration of the far off galaxy and hopefully the discovery of a new home. What's interesting is that it's here where the biggest time dilatation occurs; all this takes over fifty years to occur, but because Coop was under such high gravity in the singularity it feels like a couple of seconds to him.
