Frequency is pitch. Or how fast it oscillates. So what does the amplitude translate to in physical space? I know its volume, or the amount of energy. But what does it actually do to the air when you increase the amplitude?
It is the variation in density of the medium. In air, the waveform expresses the relative density of the air - the peak of the waveform is the max compression of the air, the trough of the waveform is the max rarefaction (minimum compression) of the air.
Air at usual density can be compressed more than it can be rarefied because sufficient rarefaction results in a vacuum. Air is "single-ended".
It would be better to say "max and min pressure" rather than "density". For sound transmitted through (nearly) incompressible solids and liquids, the change in density is negligible compared with the change in pressure.
for "normal level" sounds the pressure changes are tiny - they may be a million times smaller than the steady atmospheric pressure. Even for very loud sounds that would quickly damage your hearing the pressure changes are only 1/1000 of the steady pressure.
As AlephZero said, it's the amplitude of the changes in pressure. You could measure this with a barometer, if it could react fast enough to capture the waveform (it would be easier with a low frequency). This also puts an interesting upper limit to how loud a steady waveform can be - the low pressure could not be any lower than zero (absolute), so you'd be limited to pressure swings from 0 to about 30 psi at sea level before the sound would distort. Normal sound only creates tiny fluctuations though, so this wouldn't really have any effect unless the sound was loud enough to do things like kill people and level buildings.