Besides just sleeping, it's also used when a conversation or situation is so boring it makes you sleepy. Friends might playfully send it to each other when someone is telling a long, uninteresting story.

"Zzz" originates from the English onomatopoeia mimicking the sound of snoring, similar to "kool kool" in Korean. Therefore, it's used not only for a state of sleep but also as a strong expression like, "Stop it! This is so boring!" or as a humorous signal to end a conversation.