When a computer or other device is not turned on or connected to other devices, it is said to be "offline." This is the opposite of being "online," when a device can readily communicate with other devices. For example, if you try to print to your printer and you get one of those frustrating errors saying, "The specified printer could not be found," the printer is probably offline. You should check to see if the printer is connected properly and, yes, turned on as well.
Offline can also mean not being connected to the Internet. When you disconnect from your ISP or pull out the Ethernet cable from your computer, your computer is offline. Some programs, such as Web browsers and e-mail programs, have an option to "Work Offline." This option disables the program's network connection, meaning no data can be transmitted to or from the computer. This option was more useful when most people used dial-up connections. They didn't want their computer automatically dialing their ISP whenever a program tried to access the Internet. However, since most people now have "always on" connections such as DSL and cable modems, there usually is no reason to work offline.