Not all varieties of monitors react with linear brightness increase to linear increases in input signal.
For example if the brightness is proportional to the square of the voltage then half brightness might occur at 0.707 times the maximum voltage. In that particular case, if you had a data reading which was "x" fraction of the maximum reading, you would need to use sqrt(x) to calculate the output voltage to send in order to achieve the right linear brightness according to data reading.
This process of applying a non-linear mapping between data input and signal output is known as "gamma correction".
There is no one "right" way to do gamma correction. Fundamentally all you need is a function that maps between input data values and required output.
About the only thing you can be sure of for physical situations is that the function will be continuous and monotonic (increasing or decreasing), but it could be sqrt(), could be cube, could be exponential, could be an "S" curve.
This process of non-linear mappings to achieve different brightness is extended to digital values, in which case it does not necessarily hold that the function is continuous and monotonic. If you want to digitally map 0.3 to 0.5678 to be dark and other areas to be bright, you can do that with an appropriate calculation. Any input function that maps individual data values (or RGB combinations) into outputs in a manner that is position independent (and independent of surrounding values) is a potential gamma correction for digital purposes.
