What controls the brightness of the MCDU display and keys?
These buttons are to increase and decrease brightness of MCDU. Also, they are used to turn on and off the unit.

As explained here:


  BRT AND DIM KEYS
  Control the light intensity of the entire MCDU. MCDU power up is performed 
  with the BRT key and MCDU shut down is performed with the DIM key.


And here:


  Repeatedly clicking on the "BRT" (the top of the paddle switch) will
  switch the unit on and increase the brightness. The reverse is also
  true. Repeatedly clicking on the "DIM" (the bottom of the paddle
  switch) will decrease the brightness and switch the unit off.