Bass, mid, presence and treble are tone controls - they allow you to adjust the relative levels of notes or sounds at different parts of the audio spectrum. Low, medium, medium-high and high respectively.
Gain, in eg. a guitar amp, sets the input level to the preamplifier and tone stages.
Using too high a gain or input level accidentally causes distortion or "clipping". That can be unwanted, or with a guitar it's "overdrive", deliberately excess level causing distortion and a fuzzy sound.
Guitar amps may have switchable input channels with different gain controls for clean or distorted sounds, or a switch that changes the range of the one gain control between normal and high.
The master volume sets the level sent to the power amp and loudspeaker, and how loud you hear the amp.