ESC - Electronic Speed Controller
The ESC is the brain of your electric skateboard. It controls everything and makes all the parts working together.
The ESC main function is to vary an electric motor's speed. To do that, it's controlling the amount of power to transfer from the battery to the motor(s). It's as simple as that.
The ESC takes orders from the remote control receiver. The receiver asks for a certain motor speed (or RPM, rotation per minute), and the ESC will do its job, transfer power, until the RPM is reached.
The ESC helps to provide a smooth acceleration, required on an esk8 (you would be thrown out of the board otherwise). It won't send all the power at once, but rather send it gradually until the motor reaches the correct speed.
In the esk8 world, the ESC is also used as a regenerative braking system. It'll basically transfer power from the motor to the battery, and by doing that, slowing down the motor until it's fully stopped. Again, this works progressively so you can break safely without being thrown out of your board.
A good ESC will allow for a good progressive acceleration and deceleration. Very good ESCs are even programmable, so you can basically decide how progressive it is, how fast it goes, etc...
ESCs in the esk8 world
Most brands selling esk8 have a custom ESC designed for their board, running custom software. They are designed for mainstream consumers and often aren't able to be easily changed or customized.
Some DIYers have used ESCs that were designed for electric RC cars. They work basically the same way, except that you need a really beefy RC car ESC given the energy needed for an esk8. But given the popularity of DIY esk8, or even DIY personal EVs in general, it's getting easier to find a good ESC for a given use, without having to hack one that wasn't designed for this specific use in the first place.
A few different brands make ESC designed for esk8s. But there's one that kind of beat them all: the VESC.
The VESC, the perfect ESC for DIY esk8s
Find more details about it on the dedicated page.