Offering the HTTP service means that any vulnerability in that service becomes an entry point for attackers. So be sure to manage this service with all due diligence: apply security fixes published by the vendor, as promptly as possible. This is for both the HTTP server software itself (say, Apache) and the "site code" (a hole in the PHP code is still a hole). Apart from that, this server won't add much to your (in)security, on the technical side of things.
However, a publicly available HTTP server implies higher exposure. Most people evade trouble not by running fully patched software, but by being commoners. People from home doing Web surfing like normal people. Uninteresting schmucks. There are so many of those, perhaps billions, that nobody really gets motivated into hacking into their machines. Sure, there is a lot of automatic hacking going on; those botnets won't feed themselves ! But no real threat from a motivated, intelligent attacker. By running a Web server, you become uncommon. You may attract interest. People who run Web servers at home may have interesting data to provide; at least they made an effort to provide a service for other people.
Basically, offering such a service tends to remove a very powerful protection layer, i.e. anonymity (as in: "does not show up on radar among the masses"). Evading attacks by simply looking "normal" is, conceptually, a very unsatisfying way to protect your information assets, but it works very well; and your HTTP server will strip you from that.
An extra source of worry is that your home network is "protected" against intrusions by the combined forces of your cable/ADSL modem (provided by your ISP) and, possibly, some sort of home (WiFi) router. These devices use software which is rarely updated, and thus tends to have many security holes. You don't really want to attract attention to that.