So the way I understand what a dedicated server is:

A server that is on all the time, it is automated with scripts to have a mapcycle and a gametype cycle. You always need a computer to be on and connected to the Internet for it to work. Can you turn them off?

Yes you can turn them off.
The term dedicated is being confused with umm "full time", implying that it is running 24/7.
You can run a dedicated server from your pc, and have it running when you want.

In a broader sense, a dedicated server is a server which is provided to you by a service provider. On this server, you can do just about whatever you want (within terms of agreement), with little to no downtime. So if you get this server, you may decide to have it play a Halo Dedicated Server.

If you don't have the money to rent a server, then you can simply build your own, running a free software such as BSD or Ubuntu. Previously, I had an ancient Celeron computer overclocked to about 1.7ghz (factory was ~825mhz), with less than 128mb memory, running Windows 2000 as a dedicated server in my basement. It worked fine for several months, until it went under full load and went up in smoke. I'm sure somebody would be able to muster up some more reliable hardware nowadays.

When you're having a server acting as a dedicated server, it basically runs a render less copy of the game, handling services, scripts and map loading much like you would when you host your own game. It doesn't need to be connected to the internet, but if you want people outside your local network to connect, then you need the internet. Turning the system off is about as simple as remotely accessing through RDP, and typing 'quit' into the console, or using "shutdown.exe -i" at the command prompt.

Are you saying I can use my netbook to host games?

yes, it probably can.

and it probably will go up in smoke.

Dang.

lol, yeah, but I was looking specifically for one about games.

same concept

fixed