One typical application for enable pins on regulators is for undervoltage lockout (UVLO). The idea is that you use a resistive divider across the input voltage to this pin such that when the input voltage is too low to ensure proper operation, the enable input falls below the threshold and the regulator shuts down. However, for this to work properly, the enable input must have some hysteresis, and you will have to make sure that you don't violate any maximum voltage on this pin if one is specified (check the datasheet). Note that the voltage divider will consume some power from the input, so for battery applications the resistance should be suitably high to limit the current to acceptable levels.
Another possible use is to shut down part of a device for power savings. For example, a sensor might have a fairly power-hungry analog frontend, so in order to save battery life you may want to shut the frontend down when you're not actually measuring anything.
You can also use an enable input to implement a power-on delay by using a resistor and capacitor to ensure that the enable input doesn't cross its threshold until a certain amount of time after power has been applied. This can be useful for power sequencing, or in situations where the power supply takes some time to stabilize before it's safe to bring up the main circuitry. In this application, you may also see a diode across the resistor to ensure that the capacitor is discharged quickly at power down to avoid misbehavior during brief power interruptions.