Every connection made to your web site will require additional resources from your server. The more visitors the more resources required. Larger sites such as district sites may consider using Windows NT server, NetWare, or Unix. To even run an operating system a computer must have a certain amount of RAM, hard drive space, and processor power. Make sure you check the system requirements for the web server software you will use to make sure your computer qualifies.
Most computers are capable of doing more than one thing at a time.
You don't always need to dedicate a computer to just web serving. The decision depends of the number of hits you expect on your site and what else you want the computer to do. Now you'll need to see if you have enough network resources available. One such resource is an IP address. It is best to statically assign an address to the computer that will be the web server.