Many of the textbooks I have read analyze noise signals. We have a circuit and find the output noise RMS voltage. But there is always the "extra" step of finding the input-referred noise. Why do we need to find the input-referred noise? How does it help us any more than the output noise RMS voltage?
Input referred noise is used to determine the noise contribution of the circuit when it is used in a system. It gives a useful frame of reference. A circuit with a lower input referred noise will contribute less noise to overall system than one with a higher input referred noise.
Input-referred noise is the noise voltage or current that, when applied to the input of the noiseless circuit, generates the same output noise as the actual circuit does.
Input-referred noise is generally more useful because it relates directly to the unaltered signal. You don't have to know anything about the gain and other characteristics of the amplifier this signal is connected to in order to understand the noise level.
Put another way input-referred noise is the same as having a perfect amplifier, with all the noise being originally on the signal.