Several spells take effect on the target's next turn. Command is one example (PHB, p. 223):
You speak a one-word command to a creature you can see within range. The target must succeed on a Wisdom saving throw or follow the command on its next turn.
Compulsion has similar effects.
A spellcaster with the War Caster feat can cast these spells as a reaction (instead of a melee opportunity attack), during the target's turn. For example:
Harrek the Barbarian is within reach of Almira the War-Cleric. Harrek wants to go hit Almira's pet troll, so he moves away from her, figuring that he can shrug off any melee attack she might make. Almira casts command, with a command of "Halt". Harrek fails his Wisdom save.
When does Harrek "Halt"? Immediately, effectively ending his turn? Or on his next turn, after he has had a chance to move and attack the troll, and after Almira has had her turn and had a chance to cast another spell.
This point was raised in this question, but wasn't the main focus.