It's a visual representation of someone snoring, just like how "lol" represents laughter.
Here are some examples:
* "I'm so tired, I'm going to bed. ZZZ"
* "I'm ZZZ right now, don't call me!"
It can also be used to indicate that someone is bored or finds something uninteresting.
For example:
* "This meeting is so boring, I'm ZZZ"