What is the "Brake to Exit" feature on the Boeing 777X?
It is a system that Airbus already uses in the A380 
and some A350's. They call it BTV (Brake to Vacate).

It allows the pilot to select a certain runway exit in advance (e.g. while approaching).
After touchdown, the plane automatically brakes so it can vacate the runway at that given exit.

Airbus says:


  When the pilot chooses a runway exit point, the system indicates the estimated runway occupancy time and the minimum turnaround time. During the subsequent landing phase, and according to encountered runway conditions (i.e. 'wet' or 'dry'), the aircraft's deceleration is automatically regulated so it reaches the chosen exit at the correct speed.


(emphasis mine)

The BTE system by Boeing is a similar system with a different name. A related article in Avionics International about the B777X states:


  “We have also added new safety features like optimal runway exiting and brake-to-exit, which will allow a pilot to tie an airplane’s rollout and stopping distance to a specific runway exit,” said Kirk Scarbrough, Boeing’s 777X systems chief engineer.  


See also 


What is Brake To Vacate (BTV)?
FAST magazine from Airbus, issue #44(PDF, 10MB) from July 2009, section "Brake-to-Vacate system", pages 17-25