"Post" naturally refers to "post-production", the part after principal photography where all the editing, sound-looping, Special Effects etc. happen. "Fix it in Post" is said when you goof, but decide you don't want to re-shoot. "Forget it, we'll fix it in post" they say and move on with their lives. In post-production they will edit out the mistake, loop dialog to cover it or digitally re-master the image so the mistake never happened.