A load line is used in graphic analysis of circuits, representing the constraint other parts of the circuit place on a non-linear device, like a diode or transistor. A load line represents the response of a linear circuit connected to the nonlinear device in question. The operating point is where the parameters of the nonlinear device and the parameters of the linear circuit match, according to how they are connected while still adhering to their internal systems.
In the example on the right, the nonlinear diode is placed in series with a linear circuit consisting of a resistor and a voltage source. The load line represents the relationship between current and voltage in the linear part of the circuit while the exponential represents the relationship between current and voltage in the nonlinear device. Since the current going through three elements in series should be the same, the operating point of the circuit will be at the intersection of the exponential with the load line.
In a BJT circuit, the BJT has a different current-voltage (IC-VCE) characteristic depending on the base current. Placing a series of these curves on the graph shows how the base current will affect the operating point of the circuit.