"Next turn" means your next full turn. So if you start a turn with the condition in effect, then at the end of that turn, it is removed. If a monster stuns you on its turn, then your next turn (whether that happens in the current round or the following round) you would be under the effect of stun, and then it would go away at the end of that turn. If you manage to get stunned on your own turn, you would immediately suffer the effects, then you would also suffer from the effects on your following turn in the following round before the effect wore off at the end of that turn. This also applies to conditions on monsters.