What is Under the Gun and where the name comes from
The term Under the Gun comes from an old English expression describing being under threat — "having a gun pointed at you." In poker it describes the situation precisely: the UTG player must act first, with no information about what the rest of the table intends to do. Every other player, including the blinds who already put money in the pot, gets to react after UTG's decision — meaning UTG plays "blind" in terms of information about opponents, while they see exactly what he did.
The practical implication: UTG must choose a range of hands that wins statistically even without the benefit of position, against all the possible ranges of the players who haven't acted yet. This is why the seat is unanimously considered the hardest to play correctly, and also the most common source of mistakes for beginning players.