A player with ten or more poison counters loses the game. A Two-Headed Giant team loses at fifteen.
The rule
Poison counters are counters on a player, not on a permanent (CR 122.1f). A player with ten or more of them loses the game as a state-based action (CR 704.5c), whatever their life total is. A player with at least one is poisoned.
They come from cards with Toxic (CR 702.164), Poisonous (CR 702.70a) and Infect, and from cards that simply say to give a player a poison counter.
In Two-Headed Giant the team shares its poison counters and loses at fifteen (CR 810.10, CR 704.6b); larger teams get five more per player beyond the second (CR 810.11). In Archenemy every player keeps their own (CR 904.13c).
In Life Counter
Switch poison on for a game and every player gets a poison coin. The app knows the threshold of the format: ten for a player, fifteen for a Two-Headed Giant team, and it marks the player one counter short.