Setting aside a conviction results in the charges being "dismissed," which indicates that the judge has reviewed your case and determined that setting aside the conviction is appropriate. Please note that this is not necessarily the same thing as restoring your civil liberties, which often requires a separate application -- though by its terms, a set-aside results in the person being "released from all penalties and disabilities resulting from the conviction," with a few exceptions. Still, it is the better practice to apply for both. (Doing so will be the subject of a future post.)
If the judge grants your application, this does not mean that the conviction disappears. As noted above, the case record can still appear if someone searches for it, and some court records show up on Google searches. Thus, if you apply for a job after having a conviction set aside, and the application asks if you have ever been convicted of a criminal offense, the best answer is something like, "Yes, BUT the conviction was set aside." DO NOT claim that you have not ever been convicted -- such dishonesty will likely cost you the job, and if you are applying for a government job, may result in further prosecution.
The statute governing set-asides in Arizona is A.R.S. section 13-907.