it's the laugh in korean.
On the korean keyboard it is ㅋㅋㅋ
but if they are typing with a english board the ㅋ is in the place of the z.
Usually they use it if they are too lazy to keep switching back and forth between language modes.
Also can be written as kekeke
1: zzz
2: I am boring you?? what is "zzz"
1: it is the laugh "ㅋㅋㅋ"
Term used when something bores you.
"Homework sucks! Zzz. Really. Zzz."
Zzz is Mike speak for I'm done working and I can't be disturbed!
Me: Hey Mike, want to catch a beer after work?
Mike: Zzz!