In general, when a machine is “online,” it is turned on and connected to other devices. For example, when a network printer is online, computers connected to that network can print from it.
Recently, however, the term “online” usually means being connected to the Internet. The connection can be through a phone line, using a dial-up or DSL modem, a cable line via a cable modem, or through a wireless connection.
Example of usage – “When he bought the new game for himself, he read that in order to enjoy the complete experience, his console would be to be online at all times. This meant that he would need a stable internet connection at home and ensure that the console was always connected to it.”