How did Satoru obtain the Revival ability? Satoru Fujinuma has the "Revival" ability, which allows him to go back in time before a life-threatening incident happens. We do know that he is not able to control this power (even if he can somehow help to summon it sometimes), but do we learn at any point how he obtained it ? Or did the author mention anything about this ?
⚠ The answer below contains spoilers.

It is never stated in the anime nor in the manga how he obtained this ability. We know that after the events in the last episode, he loses it and it never occurs again.

As the Boku Dake Wiki says:


  Revival (再上映 (リバイバル), Ribaiburu, lit. "Rerun") is an involuntary special phenomenon exclusive to Satoru that allows him to jump back in time in order to rescue someone from a fatal encounter within his proximity.
  
  Empirically, Satoru's capable of responding to Revival, as it occurs involuntary and often at random times. Fujinuma described his experience as a deja vu.


http://bokudakegainaimachi.wikia.com/wiki/Revival