To sleep. I'm not sure of how many ways to use it though.
If you were sleeping you wouldn't be "z'ing."
The only way I know how, or have heard anyone use it is in the example.
Synonyms for z's
On this page, you will find 30 slang terms related to z's. Some of the top words include: z?, iunno, shlept, snoozle, buh, and 25 more.