In an amplifier, does the gain knob boost or attenuate the input signal?

It could be either when determined by marketing. Two common configurations are shown below.

^{simulate this circuit – Schematic created using CircuitLab}

Figure 1a: Fixed gain pre-amp with preceding attenuator. 1b: Variable gain pre-amp.

• 1a is simple but has the disadvantage that the noise from OA1 is constant even with the input turned to zero.
• 1b has the advantage that as the gain is reduced so is the noise.

(Gain in the example circuits is -R2/R1 or -R5/R4.)

Mostly, it's a potentiometer that selects a proportion of the signal to feed through the subsequent amplification stages like from this datasheet. Red marks by me: -

And this one from this datasheet with my red marks: -

But it can be "digital" where the action of the knob turning clicks a switch a number of times (might be subtle to tell if you didn't know) will ramp the volume up or down: -

The above from this datasheet with my red marking.

Typically (for audio) it's an attenuator placed in between portions of the circuit such that the signal level is high enough that there will not be much disagreeable background hum or hiss with the pot cranked all the way down. That also means that pot wiper noise does not tend to cause too much disagreeable scratchiness when the pot is adjusted.

You would not, for example, want to attenuate the signal going into a preamp.

In instrumentation it might directly affect the gain, for various reasons related to how much adjustment range is required, how accurate the gain has to be and so on.