Zeigarnik effect
Also said as Unfinished business, Ovsiankina effect (the resuming half)
The claim, from Bluma Zeigarnik's experiments published in 1927, that people remember unfinished tasks better than finished ones. Her colleague Maria Ovsiankina reported the related urge to go back and finish.
The popular version overclaims. A 2025 meta-analysis by Ghibellini and Meier found no general memory advantage for unfinished tasks, but it did find a general tendency to resume them. So do not say players "remember" an open quest better. Say that an interrupted task tends to pull you back, which is the part that seems to hold.
Say it
“When the player quits, save mid-quest and show that quest first when they come back. Do not nag with a notification: being asked is not the same as the pull of an unfinished thing.”
Where you’ve seen it
Civilization's "one more turn" works this way: at the end of any turn something is nearly finished, a building or a research, so there is no clean moment to leave.
Not to be confused with cliffhanger
A cliffhanger makes you want to know what happens next. The urge to resume is about a task you started and did not finish, even a dull one.