This is a subject for which I am no expert but I do feel I have a decent enough grasp on the basics to help others.
DC brushless motor concepts
Let me start by stating the obvious, DC brushless (BL) motors have revolutionized the rc hobby, especially in aircraft. They small, light, powerful and efficient. These motors come in nearly 100s of different sizes and configurations for use on anything from micro aircraft to 1/4 scale aircraft. Simply put we would not be able to do what we do today in RC without modern BL motor.
How a BL motor works (simplified)
A BL motor is what it sounds like, a motor without brushes. One portion of the motor is fixed and contains the wire windings, while the other part spins and contains permanent magnets. The motor spins by alternating the 3 inputs, 2 at a time. It basically "steps" from one winding to the next. A brushless electronic speed control (ESC) adjusts when and how the switching happens in order to change the rpm and power of the motor.
For more in-depth information check out this article at WikiPedia.
Inrunner or outrunner?
There are basically 2 main types of BL motors out there, inrunners and outrunners. On inrunners the core surrounds the magnets and on outrunners the magnets surround the core. The most popular rc motors are outrunners and are easy to spot because the outside "can" of the motor spins. Aside from the differences in physical design, the main difference between the 2 types is that inrunners are designed for high rpm, low torque applications, and outrunners are designed for high torque, low rpm applications. As such 99% of BL aircraft motors will be outrunners.
Changing the direction of a BL motor
If you want to change the direction of a brushed DC motor, you simply swap the motor leads. Basically the same applies to BL motors. The difference is that there are 3 wires instead of 2. To change the direct you simply swap any 2. This is easily illustrated by drawing it. Draw a triangle and number each corner 1, 2 and 3. Then count 1 - 2 - 3 -1 - 2 - 3 - 1 ... to see the direction. Now swap any 2 numbers and see how it effects the direction.
Some ESCs will also allow the direction to be set as one of the options during setup.
Brushless motor terminology
Next up is the ever confusing BL motor terminology. Seems like every motor manufacturer uses a different method to name their motors. This can make it a challenge to find the right motor but it turns out that all motors share the same basic method of describing the specs. Let me first cover the important commonalities and then I will touch on a few of the naming conventions.
Applying the terminology to selecting a motor