Line regulation is the ability of a power supply to maintain a constant output voltage despite changes to the input voltage, with the output current drawn from the power supply remaining constant.
It is desirable for a power supply to maintain a stable output regardless of changes in the input voltage.
The line regulation is important when the input voltage source is unstable or unregulated and this would result in significant variations in the output voltage.
[1] In the regulator device datasheets the line regulation is expressed as percent change in output with respect to change in input per volt of the output.
Moreover, the line regulation of the device expressed in the datasheet is temperature dependent.