no, you can host files on your computer to the rest of the world...
I'll assume that you have either a modem attached to your server computer, (which is then conected to some sort of network for any other computers in your house).
all you need to do is open port 80 on your firewall and have it directed to your server machine, (this would either be in your firewall settings, (windows firewall or any other firewall program).
assuming that you have a hardware router then there should be some sort of settings on the router, (usually accessed via a web interface) that will let you make port 80 point to your server...
for an address that is easier to remember than your IP address (and one that won't change) check out
www.no-ip.com it's free, easy to set up domain names (e.g
www.scienceguy.no-ip.com) that point to your computer rather than some random free web space.