BEC (Battery Eliminator Circuit) But... This is not what it does anymore or its not really the correct terminology anymore. What people are doing is running more of a voltage regulator.
Say your brushless revo is running a 4s Lipo 14.8 volts. Well you can't put that kind of power to a servo. So you run a (BEC or Voltage Regulator) and your servos are now only seeing the regulated voltage(normally 6.0V)
That's the basic idea.
Maybe someone with more knowledge can elaborate more for you.