A Half-Night Stand is a casual hookup where one person leaves soon after sex rather than staying the night.
A half-night stand is a one night stand without the sleepover. After sex, one person heads home rather than staying until morning.
The appeal is skipping the awkward morning after. No shared breakfast, no lingering, just the encounter itself and then back to your own bed.
For some people it feels cleaner and more honest about the casual nature of the hookup. For others, the quick exit can feel cold.
The key, as with any casual encounter, is that both people are on the same page about what it is and is not.
If staying over would imply more than you mean, leaving can keep things clear. Just be upfront so the other person does not read the early exit as rejection.