I am a non-enforcement employee of the NYPD.
The rules, regulations, and procedures of the Department are compiled in two books, called the "Patrol Guide" and the "Administrative Guide". Because of court decisions, changes in the law, and so on, changes in the rules/regulations/procedures occasionally must be made. When a change is made, a "General Order" is issued, documenting the change. The General Order remains in effect as such until the revised rule/regulation/procedure is incorporated into the next Guide update (which usually happens once per year). However, it is often the case that a procedure becomes known by its General Order number, even years after it has been incorporated into the Guide. This is the case with General Order 16, in the show - by now, it has been incorporated into the Guide, but it became so well-known as a General Order that the original name has 'stuck'. (Similar things happen to standardized paperwork; it has been decades since a complaint report [report of a crime] has borne the form ID number "61", but you still hear them called "sixty-ones".)
I can guess at what current procedure is being referred to, but it's not actually relevant for the purposes of this question. The phrase "You're being G.O. 16'd" simply means that the Department is invoking the provisions of the Guide procedure originally promulgated as General Order 16, and the person being spoken to in the scene is the target. The subsequent statements imply that the procedure in question is a disciplinary investigation, and if the target of the investigation is caught lying, it will be sufficient grounds, in and of itself, to get the target fired.