Those new to VEX may feel a bit at sea with VEX's different motor options. First things first, for a competition robot, only use a 2-wire motor 393 (or 3-wire servo). If a website is mentioning a 3-wire <em>motor</em>, that's an old, discontinued product that should not be used in competition, as it is less powerful than the 393 motor.
The links included here are to products on Robot Mesh, a VEX reseller. Resellers sell exactly the same products as VEX Central Command, and at the same prices. Different resellers have different deals on shipping and if there is one closer to where one lives, then packages arrive faster than if ordering from VEX direct.
On to the motors. VEX provides the option of buying the 2-wire motor 393, or a package of the 2-wire motor and a motor controller. So what is the motor controller thing and when is it needed? On the VEX cortex, there are 10 slots in which to plug motors. Slots 1 and 10 have the motor controller built into the device; slots 2-9 do not, and require external motor controllers (see image below).
So what does this motor controller do, anyway? Well, the motor controller makes use of what's called PWM to control the speed of the motor. PWM stands for Pulse Width Modulation, and it turns the circuit (battery-to-cortex-to-motor) on and off in rapid succession. It's a very fast version of what a microwave does on 50% power. The microwave is not actually outputting half of the power of “High”, but rather it's cycling its one fixed level of power on and off about half the time. Motor controllers do the same thing to control the speed of a VEX motor; setting a VEX motor to power 64 (half of the maximum 127), means that the controller is sending power to the motor half the time and sending 0 power half the time; this all happens in such rapid modulation that there's nothing noticeable going on to the outside observer. (See the (coming soon) motor article for more detail.)
VEX motors have a plug on the end with 2 wires, a red and a black. The motor controller has one end with a 2-wire plug that connects to the motor, and the other end has 3 pins (red, black, and white) that plug into ports 2-9 on the cortex.
For slots 1 and 10, that whole 3 wire-to-2 wire conversion goes on inside the cortex. The motor controllers built into the cortex function better than the external controllers; for the details, please read this article on Ports 1 & 10 (soon to be included in this wiki). The upshot is that it's unwise to have multiple motors on a robot that must work in unison plugged into a combination of internal and external controllers.