|KV as we use it refers to the rpm constant of a motor - it is the number of revolutions per minute that the motor will turn when 1V (one Volt) is applied with no load attached to the motor. In summary, we call it revs per volt - but do not think you will obtain those revs when you attach a propeller; obviously the revs will be reduced because of the load.
I have seen this aspect of a motor referred to as KV and Kv and kv - just be sure not confuse it with kV which stands for a kilo-volt.
What does the KV tell us? Well it is related to the power out from a motor, or more usefully the torque level of a motor. It is determined by the number of winds on the armature (or turns as we sometimes call it) and the strength of the magnets - you see, there are so many variables with electric motors. So KV allows us to get a handle on the torque we can expect from a particular motor.
In summary, a low KV motor has more winds of thinner wire - it will carry more volts at less amps, produce higher torque and swing a bigger prop.
That may sound confusing, but compare it with a high KV motor which has less winds of thicker wire which will carry more amps at less volts and spin a smaller prop at high revs.
Let me give you an example:
A Hyperion 3025/6 is what we call a hot motor - it has only 6 winds of thick wire and is made to carry big amps at low volts (specifically what we need for the 7-cell electric glider competition).
The 3025/6 has a KV rating of 1255, meaning that the motor will spin at 1,255 rpm per volt with no load (not recommended for brushless motors - never run them without a load - it is a theoretical value).
Check the specs on the 3025/6 and you will see that it will spin a 12x6 prop at 7,900 rpm on 7 cells and draw 48A - giving 350W. You might want to push the amps with this motor and fit an even bigger prop to give you more Watts for competition use because it will take more amps - it is able to take 65A for up to 60 seconds or 100A for up tot 10 seconds.
Compare this with a Hyperion 3025/8 - that is the same size motor physically (armature 30mm diameter and magnets 25mm long), but it is wound with 8 turns of thinner wire. It has a KV rating of 985 - much lower than the hotter 3025/6. It will spin a 12x6 prop at 6,900 rpm on 7 cells and draw only 27A producing 249W. This motor has more torque and you might want to increase the voltage to take advantage of that characteristic, but watch the amps because this motor has an amps limit of 52A for 60 seconds.
These motors are quite close in specs, but you can see the difference. The point is that the high KV motor would be used to give high power for short bursts in competition gliding, but the lower KV motor has more torque and is better suited to a sports application, like powering a sports cabin model.
In fact, for sports use you might even go to the 3025/10 which has a KV of 815 because it is even more torquey and would work well on 3S with a 12x6 prop at 31A and 324 W.
So - you can see that the KV figure is useful in helping you choose a motor for a particular application. It is particularly useful when considering two motors of exactly the same size but different windings.
When considering motors of different sizes, it is just another figure in the electric power jig-saw that allows you get a handle on a motor and its uses. You might come across a larger motor such as a Hyperion 4035/10 and you will check the KV rating at 405. Hmmmm - that's seems like a low KV, but let me check the prop sizes and the useful current range for that motor when considering it. Let me compare it with a 4035/14 and I find that the 14 wind motor only has a KV of 299 - so you can see that bigger motors have a lower KV rating than smaller motors and operate at higher volt ranges for a different purpose. A 4035 motor will use 6S to 8S (higher voltage LiPo batteries) and fly a .60 size model weighing up to 6.0kg.
In essence the KV figure allows us to compare similar motors - most of us use a particular size motor (like the ones available for electric glider competitions), so find the KV figure useful in making comparisons.
To complicate matters, if you take a high-KV motor and add a gearbox you make it in to a lower KV motor! For example, my Elios 56 geared 5:1 used in my competition electric glider is a 5600 KV motor, but the gearbox makes it lower KV and it swings a 17x13 propeller! It is a 5600 KV motor when considered without the gearbox, but it is a 1120 KV in effect when a 5:1 gearbox is added to it. The motor is still doing 5600 rpm when one volt is applied to it, but the output shaft of the gearbox is doing 1120 rpm. You can still see that this is a low voltage/ high current motor because if you apply 7 volts to the motor it will do 39200 rpm without a load (not that we ever do that - we should not run brushless motors without a load) and that is quite a high revs level. Inner-runner motors like this will run at quite high revs, but Plettenberg say that there is a limit to the revs capability of their inner-runners and it is about 70,000 rpm!
Outer-runner motors on the other hand are low rev, high torque motors and are not intended to run at very high revs like some inner-runners are. Outer-runners are generally limited to more like 15,000 revs and this is reflected in the relative KV ratings.
So - there are horses for courses, and the KV rating of a motor is one factor that gives us an indication of the way it is meant to be used. You would not use a low KV motor in a ducted fan because you need high revs with a little impeller. You would not use a really high KV motor in a glider (unless it is geared) because you want to swing a large prop and obtain high torque.