No, no don't get confused.
I know what a printer is.

Anyways, I have a question though.
I have successfully acquired myself a shared printer in just 30 min. through steps from XP to Vista. I was wondering when my computer that is connected to the printer must be on so the other computer can print. I try turning off my computer that is connected to the printer while the printer is on, but the other computer cannot print. I'm confused.

This my first time "Printer Related" so please try not to use technical terms.

May the Nuke Fall!

Please note that I have all the XP and Vista related matter all covered so I just need to know why about what I stated above.

I try turning off my computer that is connected to the printer while the printer is on, but the other computer cannot print. I'm confused.

You have answered your own question. You are sharing Computer A's printer. If Computer A goes away (powered off) so too does its printer.

What you need is a network and a print server. The print server attaches to the network as a networked device, not as a shared device. The printer attaches to the print server. Then all computers print to the networked printer independently of any other computer. This is big because the (1) No sharing is required - better security, (2) the printer does not attach to or depend on any computer for power or network connection, (3) all users can print at the same time and server will sort out order, (4) The printer can be physically located in a central location (not on your desk), convenient to all.

If you don't have a router, get one. Some have print servers built in.