A gain stage is an amplification stage. As the audio passes through various devices, it inevitably goes through gain stages to boost the signal.
When using a dynamic or ribbon mic, the first gain stage is the preamp. A condenser microphone requires a current, generally 48 volts, which is called phantom power, and this current is used to power a gain stage built into the microphone.
Not all gain stages are equal. The way audio amplification works, in a nutshell, is like taking a picture of a picture. The source audio that’s being amplified actually gets discarded. It passes through a tube, or a transistor, and then is shunted to ground. But while it is passing through the tube or transistor, the signal is duplicated at a higher voltage. So, just like taking a picture of a picture, there will always be imperfections. The quality of the tubes, the quality of the transistors, the overall design of the circuit will all have an effect on the accuracy and the tone of the amplified signal. Usually, the goal is to amplify the signal as precisely as possible, with minimum distortion or coloration of the audio.
Sometimes, however, the inaccuracies can have a desirable effect. The most common example of this is in guitar amplifiers. They are often designed to over amplify the signal which causes high amounts of distortion.
Many microphone preamps are also designed to impart a certain character to the sound, which may suit a particular voice or musical style which the engineer is aiming to achieve.