The family of LSI-55's was designed for applications that require a confirmation of whether a device is actually operational (on, active) or not, that can not be directly observable. Let's look at the following example: a simple On/Off switch running a motor in a remote location. Consider the following two circuits: Circuit 2 uses the typical pilot light and circuit 1 the LSI. In circuit 2 the pilot light will only indicate if power is available for the pump to run. In circuit 1 using the LSI not only indicates if power is available but also indicates  that the motor is running. By sensing the current that the motor is drawing the entire motor wiring circuit, including the motor, is tested for proper operation. If, after the motor switch was turned on, the LSI did not indicate red, then the pump is not running and a fault condition exists. In addition, also note the position of the LSI. The LSI is installed before the on/off switch, unlike the pilot light circuit which is installed after the on/off switch. In this position the LSI is constantly indicating green if power is available.
The best way to learn about the Load Status Indicator and to see how to use the different models that are available is to study the application notes.
Load Status Indicator
What is the Load Status Indicator?