He's talking about your server logs, and they are wherever your host puts them (your host will know if you don't).
You'd have to go to the logs for the day in question, see what IP accessed the page needed to delete a topic, and then compare that IP to the IP on record for your moderators... assuming that you have that option turned on, and you don't have more than one sitting behind the same proxy server, or on dial-up, or any of a number of interesting scenarios that could cause an incorrect/misleading result.
Having said that, it might be worth looking into just the same as sometimes you get lucky...