A deprecated function is a function that is in the process of being thrown out (and/)or being replaced by something else in a programming language. It's usually still working in your current version, but it may become obsolete in the next update of the programming language (PHP in this case) ... or in the one after that. In other words, declaring a function to be deprecated is a warning that your source code will soon get fucked. But preg_replace() was thrown out years ago. I.e. when the warning actually shows up in your output, you already are fucked.
If that happens, your entire page may malfunction over that error. However, in this case, it just seems to be a script that is loaded via the include function, so only the stuff you include seems to crash. I've just realised that scrabulista was talking about the LatinD main page:
That page was not affected by any forum update, and the last time it got updated might be before some members of this forum had even been born ... and it's questionable whether that page is of any use at all, anyway.
What you see there is the included script crashing over a function that is no longer in use.
What preg_replace() used to do was to replace a string. For example, whenever you post a pure URL, you'll notice that the forum will turn it into a link, possibly with even more information that it can retrieve from that site. That's because the forum script notices that there is a URL and replaces it with a more sophisticated kind of link.*
The same was done on that page as far as I remember. "Latin Forum Highlights" linked to a couple of threads on this forum.
(At least that's my analysis as an outsider. That's what it looks like. Obviously, I can't read the source code)
*A simpler example would probably be that whenever you write quid malum, it gets replaced by quid malum ... or vappa being replaced by vappa.