A game round is the whole sequence that follows one paid stake, from the spin to the final settled result. It includes any cascades, respins or bonus round the spin triggers.
The term matters because several rules apply per round. A game's max win is the most it can pay on one round, including features. Your result for the round is the total paid minus the stake that started it.
Regulators and test houses use the closely related idea of a game cycle when setting rules on speed and stakes. In Great Britain, stake limits apply per game cycle, and extra stakes taken inside a feature count towards the limit.