In general, something is said to be online if it is connected to some larger network or system (which is implicitly the "line", though this interpretation is often useless). Several more specific meanings exist:
In common parlance, the larger network in question is usually the Internet, so that 'online' describes information that is accessible through the Internet.
In a system for the performance of a particular task, an element of the system is said to be online if it is operational. For instance, a power plant is online if it is supplying power to the power grid. Alternatively, a section of road may be said to be online if it is open to traffic.