How does Clara Oswin Oswald die twice?
We know that in all of time a person can die only once, and we see Clara die in 2 episodes of Season 7 (Assylum of the Daleks and The Snowmen)?
My question is how is this possible?
The Doctor's Name episode finally addresses this. I suppose I'll just summarize:
Throughout the events of the episode, the Great Intelligence, a somewhat recurring villain, finds the Doctor's personal time stream, which is basically his entire life.
Anyone who enters the time stream would die, but thousands of copies will be sent through the Doctor's life. The Great Intelligence seeks to do so, and command all of his copies to kill the Doctor in every possible moment, turning his entire life into a burning hell, thus finally getting revenge (the Great Intelligence doesn't mind dying as long as the Doctor suffers).
Clara saves the Doctor by following the Great Intelligence through the time stream. Thousands of copies of Clara are spread throughout his life, all with the purpose of protecting the Doctor. Supposedly, the Clara at the Dalek Asylum and the one of victorian London are two of these copies that somehow end up helping the Doctor.
tl;dr - they're clones.
They are separate characters, played by the same actress, although sharing the same name. A third character (again, with the same actress and character name) has
recently become the Doctor's latest companion. There is at least on hint that she may be the same Clara who died in the Dalek episode - she gave herself the nickname 'Oswin', which that Clara used - but that may well be another weird coincidence.
Why these (biologically-unrelated) characters share a name, personality, and so on is an ongoing mystery of the show.