Battery eliminator circuit
In household gadgets, BEC was one of the early terms for a mains -> DC power supply. In RC, it is typically a device that takes a LIPO battery's 10-15V and converts it with a solid state DC-DC converter to power electronics that need 5V. Most simple setups use a BEC inside the ESC, and are sufficient to power the Rx at 2-3S, but more complex, higher voltage setups may require an external 'UBEC'. A UBEC can allow you to fly an Rx & servos, an autopilot, or even an FPV setup at 5V while the motor happily gulps 16V from the same battery. Without a special UBEC setup, the integrated BEC can't cope with high current demands, and a second battery may be required in order to power these secondary electronics.
The Rx and BECs typically require something in the general vicinity of 5 volts to operate. Most ESCs contain small integrated BECs working at 5V or 6V to drive the Rx, and through it, the servos. Usually these are based on a linear regulator.
 Linear Regulator
WP says this about linear regulators:
- Linear regulators can only output at lower voltages from the input. They are very inefficient when the voltage drop is large and the current is high as they dissipate heat equal to the product of the output current and the voltage drop; consequently they are not normally used for large-drop high-current applications.
These are extremely cheap, and work just fine at reasonable power when the amount of voltage to step down is small. When the voltage jump is larger, a linear-regulator based BEC has trouble. While the components may technically be able to convert 14.8V (4S LIPO) to 5V, the amount of heat bled off internally would be extremely high per power delivered to the servos, so tiny low-power servos might be practical with a linear regulator, but not much more.
 Switchmode Regulator
An alternative to the linear regulator is the more sophisticated solid state switchmode regulators. Switchmode regulators function the same as the second stage of your computer's power supply, and have been improved a lot over the last decade or two as solid state circuitry replaced large capacitor and inductor banks. They are now capable of extremely high efficiency (75%-95%) over a wide range of voltages.
An increasing number of higher-end ESCs will include integrated switchmode regulators instead of the cheaper linear regulators, but this is still a minority of models. Any BEC that operates in switchmode can be termed an 'SBEC', whether internal or external.
- Note: A switch-mode regulator is known to generate some RF signals which may pose interference problems. The problem is highly model and band-specific, however.
 external 'Universal' BEC (UBEC)
Most people running a 4S and greater LIPO do have ESCs that use only linear regulators, and so they will resort to external 'Universal' BECs which are generally *much* higher current, more capable units with a large permissable input voltage range, due to their switch-mode design and larger heatsunk components allowable by an external case.
As mentioned, for higher cell-count LIPOS (generally above 2S or 3S), the alternative to a UBEC or an ESC with an integrated SBEC is a dedicated Rx battery at 2S.