Air modes control how the game's air simulation operates.
TPT's air simulation has two components: pressure and velocity. Each can separately be turned off, resulting in interesting and odd behaviours.
Here's a list of all air modes.
The default air mode means that both pressure and velocity are used and everything is kept up to date.
This disables pressure simulation (I'll leave it as an exercise to the reader to clarify its effects.) Note that pressure still exists, but the effects high and low pressure have on their surroundings are not simulated.
This disables velocity simulation. Velocity still gets assigned to grid cells, but the effects of velocity are not simulated.
This disables all air simulation.
Both pressure and velocity get assigned to grid cells (and particles are affected by that), but neither has its effects simulated. This means high pressure does not dissipate, and air velocity doesn't push forward.