Reverse and flip means printing the photograph backwards (reversing it). Or printing it backwards and upside down. The viewer doesn't know it's been reversed (a person photographed from one side is now looking the other way). Depending on the image, the viewer doesn't necessarily know it's been flipped (turned upside down). It's a technique made much easier with digital photography.
Editors sometimes reverse a picture for purely practical reasons of layout. A face looking off the edge of the page pulls the reader's eye away from the story, so flipping the image to make the person look inward, towards the words, can sit better on the page. That much is an old and harmless trick of design.
But here is where you must stop and think hard, because reversing a photograph can turn it into a lie. The moment you flip an image, everything in it swaps sides, and if any of that detail matters, you have falsified the record. Writing and signs become back to front. A scar moves from the left cheek to the right. A wedding ring jumps hands. A cricketer who bats left-handed appears to bat right. Cars seem to drive on the wrong side of the road.
So the rule is simple and serious. Never reverse or flip a news photograph if doing so changes a single fact the reader might rely on. In news, the picture is evidence, and you do not tamper with evidence. If a face really must look the other way for the layout to work, find a different photo, or run it as it is. The neat page is never worth the broken truth.
And one last caution for the digital age: just because the software makes flipping a photo as easy as one click, that does not make it honest. The ease of the tool is exactly why you need the discipline.