A BEC reduces input voltage to a lower output voltage. BEC stands for Battery Eliminator Circuit because by reducing the flight battery pack voltage down to the lower voltage needed for the electronics, for example, it "eliminates" the need for a separate lower voltage battery just to power the receiver/flight controller.
Many ESC's contain a BEC. This is from pre-multirotor days when a battery powered rc craft had one motor and one ESC. The power was fed to the ESC and then back to the receiver and/or flight controller at a lower voltage. That's why you see instructions on a lot of multirotor ESC installations to "cut the red wire". That's the wire that feeds power back but on a multirotor with multiple ESCs you only need power from at most one ESC/BEC.
On some multirotors like DJI/Naza, a separate BEC provides electronics power and the DJI Opto ESCs don't contain BECs, so no red wire to cut. The BEC on a Naza system is part of the VU that has the LED.
While we're defining stuff, an Opto ESC means that the ESC contains a point in the circuitry where the hard wired pathway is briefly converted to an optical path. This is supposed to act as a sort of filter and reduce noise being passed.
