Gain is the amount by which an audio signal is amplified. On an audio interface, the gain knob controls the input level of the preamp — turning it clockwise increases amplification. The goal is to set gain high enough that the signal is well above the noise floor, but low enough that loud moments do not clip (distort).
A good target for recording gain is a peak level between -18 dBFS and -12 dBFS on your DAW's level meter. This leaves headroom for unexpected loud moments while keeping the signal comfortably above noise.
Gain staging refers to managing the amplification at every stage of the signal chain — from mic preamp through the interface to the DAW. Poor gain staging (too little at the mic, too much at the DAW) amplifies noise. Correct gain staging (appropriate level at the source) keeps noise minimal throughout.
Gain is different from volume. Gain amplifies the signal before digital conversion; volume adjusts the signal after it is already digital. Increasing DAC or plugin volume does not affect the noise floor of the recording — but increasing preamp gain does.