A Soft Reset is a term given to when a game is reset via input. There have been a few soft resets that happened in the Twitch Plays Pokemon Streams.
Twitch Plays Pokemon RedEdit
The only soft reset that happened in the Red stream occurred early on. Because commands were coming in so quickly, the game interpreted a string of start + select + a + b as simultaneous and triggered a Soft Reset. The Streamer quickly noticed and reverted the game to the most recent save, and thereafter disabled the use of 'select', which was quite useless in terms of the stream.
Twitch Plays Pokemon EmeraldEdit
When the Emerald stream began, the select button was enabled once more. This caused numerous resets to happen at the very beginning of the game, deleting recently created characters. Not long after A was created, the Streamer quickly disabled the select button once more, so no more soft resets would occur.