Airbursting is when an explosive detonates in the air. With nuclear explosives, this means that the entirety of their explosive energy is able to flow through the atmosphere instead of being absorbed by the ground, meaning a much larger boom with little to no lingering surface fallout.

As far as HBM goes, the ability to set bombs/missiles to airburst could trade a much larger kill / inferno zone for an almost 0 fallout range - or something to that affect.

Airburst nukes still release fallout, just much less over a much wider area, so I suppose the fallout radius could also be expanded to be much larger, but the actual environmental radiation from that fallout would only be a fraction of the radiation from a surface burst, and cause no contaminated blocks to spawn.
It would also be cool if the fallout from larger nukes was less than the fallout from smaller nukes, because with larger nuclear weapons, more of the radioactive material is flung up into the stratosphere, or even as far out as the exosphere with thermonukes.

One thing to remember is that most radioactive fallout is not produced by the fission reaction taking place within the weapon, but rather from neutron activation of vaporized ground materials. The distance that the neutrons from the explosion travel also tends to be roughly equivalent to the radius of the fireball, so an explosion that goes off high enough that the fireball fails to reach the surface will generate little to no fallout.