To engage in the activity of sleeping. This usually occurs after long periods of strenuous activity and/or sex. However this usually refers to a more deep sleep than that of a lightsleeper.
Nigga I be hustlin all day. Fo realz, man I can't wait to hit muh shawty up, do tha dirty dirty and then get muh Z's on.... fo real.
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.
Slang: I'm goingto cop me some z's
Translation: I'm going to get some sleep