What does “Require approval” actually change?
It holds every photo and guestbook message for you to publish by hand, instead of publishing them once they pass their check.
With it off, a photo or message that passes its content check is published automatically. With it on, it passes the check and then waits in your moderation queue until you publish it.
It is not a safety switch — the content check runs either way and anything it blocks never reaches you or the gallery. It is an editorial switch: it decides whether you see everything before your guests do.
The cost of leaving it on
Nothing appears on the slideshow, in the gallery or in the guestbook until someone works the queue. At a party that someone is usually you, and you are usually busy. Most hosts are better served by leaving it off and removing the occasional photo afterwards.
The setting is on the Moderation tab and can be turned on or off mid-event. Turning it off does not release what is already waiting — those still need publishing.
A school can switch it on so that a member of staff publishes every photo: see school event photo sharing.