When referring to an electric device that can be connected to another one, such as a receptacle, line refers to the wires feeding it from the panel, which is upstream from the device in terms of the flow of electricity. On the other hand, load refers to devices on the same circuit that are downstream of the one in question. A second meaning for load is the magnitude of the energy consumed by the devices on the circuit.
Distinguishing between line and load isn't always necessary. For example, a conventional wall switch -- which is a single-pole, single-throw switch -- works equally well whether you attach the live circuit wire -- line -- to the top brass terminal or the bottom because the switch has only two positions -- open or closed. The terminal connections are directional on a double-throw switch, on the other hand, because it can transfer power between different loads. The line and load terminals are clearly marked on such a switch, and the live circuit wire must always be connected to the line terminal.
Line and load terminals are also clearly marked on a ground fault interrupting outlet because the outlet contains a breaker that interrupts the current when it detects a current surge. Interchanging the line and load wires on a conventional outlet has no effect on the outlet, but doing so on a GFI outlet renders the breaker ineffective and creates a dangerous situation because the outlet won't give the protection it's designed to give. When daisy-chaining a pair of GFIs in a circuit, the load wires from the one upstream in the circuit must be connected to the line terminals of the one downstream, or the one downstream won't function properly.