Basically put, When you swing an object like a sword through the air it causes a disturbance and creates a swooshing noise. The shape and size of the object as well as how its actually swung will have a great bearing on the sort of noise it makes and with sword arts, there is a particular noise that is associated with good technique. This noise when referring to the katana is called 'TachiKaze' which translated approximately to 'sword wind'.
As long as the sword is properly shaped and the technique of the user good enough, the noise that comes from the sword sounds like a very satisfying whistling shriek. If these criteria are not met however, the sound can come out all flat like a dull whoosing noise.
This little nuance has been used my martial artists for years to tell if their hasuji and the motion of the sword are correct although it is generally accepted that tachikaze alone cannot be used reliably to measure performance. Regardless of this, many people use it to gauge the angle of their sword and whether or not their edge alignment is good. Its not perfect, but it's good enough.
Of course it's not only the technique of the user that has an impact on how loud or clear this whistling sound is. some katana have bo-hi, or grooves cut along the shinogi, which can dramatically affect the volume and clarity of this audible feedback and this is one reason why practically all iaito have them. The bo-hi have to be well defined, being cut cleanly and evenly on both sides if they are to be of use which is why if you are considering buying a sword for dry cutting practice, it is important to make sure it is one of quality or else you risk training in poor technique.
As a cutter, I have used tachikaze in my dry cutting practice and found it to be most useful. The problem with being a cutter is that I often run out of targets. I end up with a lot of recycling ;) Dry cutting is a staple part of my sword practice diet and the audible feedback that I get from it is helpful and very satisfying.