In January 2014, Steven Moffat provided some insight in an interview on how Sherlock faked his death:
As we keep saying to people, I do
think there was -- I can now say this -- a measure of nonsense going
on. He's falling off a building. He has one objective -- that is, not
to hit the sidewalk. That's it. That's the only thing he can do.
Didn't anybody notice that there's a whole building between John and
the point of impact? So obviously something got in the way. That's it.
It wasn't going to be anything else. The TARDIS wasn't going to fly
in. That wasn't going to happen."
Since Moffat's explanation best corresponds with the final explanation provided in the episode itself, I think the official answer is--disappointingly--that Sherlock jumped on the airbag shown in @howlers answer.
His lackluster answer fails, though, to address a number of different plot holes. For one, what happened with the assassins set to kill Lestrade and Mrs. Hudson?
ANDERSON: And what about the sniper aiming at John?
SHERLOCK: Mycroft’s men intervened before he could take the shot. He was invited
But according to The Reichenbach Fall, on the roof:
JIM: Okay, let me give you a little extra incentive.
JIM: Your friends will die if you don’t.
JIM: Not just John. (In a whisper) Everyone.
SHERLOCK: Mrs Hudson.
JIM (in a whisper, with a delighted smile): Everyone.
JIM: Three bullets; three gunmen; three victims. There’s no
stopping them now.
JIM: Unless my people see you jump.
We have little reason to believe that Sherlock could anticipate three assassins, as he likely was hearing about these assassins for the first time on the roof. But by sheer luck, Mycroft and his men were able to locate one sniper and successfully coerce him to call off the other snipers. It turns out there was only a single hired gun watching Sherlock rather than the multiple people ("my people") he claimed needed to witness Sherlock jump. Seeing how Moriarty did not establish a pattern of lying (nor did he need to), this seems less realistic.
Further, Sherlock did not anticipate Moriarty's suicide. He spoke the following words to John, which seems unlikely a line to lie about:
SHERLOCK (voiceover): But the one thing I didn’t anticipate was just
how far Moriarty was prepared to go. I suppose that was obvious, given
our first meeting at the swimming pool – his death wish.
But he also says he planned out for likely scenarios:
SHERLOCK (voiceover): There were thirteen likely scenarios once we
were up on that roof. Each of them were rigorously worked out and
given a code name. It wasn’t just my reputation that Moriarty needed
to bury – I had to die.
Put another way, Sherlock admits he didn't anticipate Moriarty dying, but he had thirteen scenarios planned for; one of which involved an empty street, an enormous blue airbag, and a taxi driver letting Watson out exactly at the right place. With Moriarty potentially alive, could this have been a plausible idea?
I think Moffat got outmaneuvered by the most fanatic viewers, and conceded early on before filming there were more fitting theories out there, but they were unable/unwilling to pull it off in the timeslot and writing:
As to the theories that were presented online, Moffat says he is
aware of them, but that for the most part, the audiences explanations
are far more complex than what the show ultimately needed. (emphasis mine)
"Needed" being the operative word, as there are many people perfectly satisfied with this explanation and a much smaller minority who are severely outraged at its incompleteness or implausibility.
Going deeper into the meta, I think Moffat knew he was denying us sufficient closure. As we as viewers find holes in the story and receive no answers, Andersen finds holes in the story and Sherlock abruptly disappears, leaving Andersen to completely break down. Of course, Sherlock fanatics are Andersen in this metaphor. /fanaticism