Here are some terms used in RC models
"Electronic speed contoller" aka ESC
What does it do?
It converts RC servo pulses (pulse width only matters, 1500us = centre, approx 1000 = left, 2000 = right) into a speed, often with reverse, so that it can drive between full speed reverse, stopped, full forward. These usually control brushed (DC) motors, but versions for the "brushless" motors are available too (which often only drive in one direction, they are intended for RC aircraft).
Why is it called "electronic" speed controller? Surely that's redundant?
No. Originally RC models used either a petrol engine (in which case, the engine is the speed controller, and servo operates its throttle) - or a second battery with a primitive electro-mechanical speed controller - essentially a variable resistor with a servo attached.
So the "electronic" means that it's fully solid state - no moving parts.
"Battery eliminator circuit" aka BEC
WTF? It is apparently the RC term for a voltage regulator. Just a voltage regulator.
So why is it called a BEC?
Because originally models used two batteries, one for the radio receiver and servos, another for the main drive. The traction battery was much bigger and generally rechargable (NiCd chemistry was common before lithium cells were good). The radio batteries sometimes used primary cells, or a different form of rechargable e.g. AA or standard cells.
The BEC essentially eliminates the secondary, or RC receiver battery, by regulating the voltage from the traction battery down to a stable voltage for the receiver (the receiver will probably want 5v, but the traction batteries are often 7v or higher)
The two-batteries scheme is probably somewhat obsolete, especially on flying models (the BEC is generally a lot lighter than a second battery).