How do Rapid Exit Taxiways improve aircraft movements?
See this related question.

Rapid exit taxiways (or high speed exits) enable aircraft to leave the runway at speeds up to 50 or 60 kts depending on the runway and aircraft type (50 kts even in wet conditions).  

They have a long, constant radius rather than a 90 degree turn.

You might find this FAA presentation useful.


Source: airlinepilots.com forum.

The purpose is to enable a landing aircraft to vacate the runway more quickly without having to slow down to "normal" taxi speeds.  A large aircraft like a 777 might need to slow to 10 or 15 knots to take a right angle turn.  This would mean spending longer on the runway slowing down to that speed.  

Since the aircraft next on the approach cannot land until the runway is clear, this enables closer spacing of landing aircraft.

Aircraft type, airport restrictions, operator standard procedures and weather can all impact what "high speed" means but it is always faster than the 90 degree turn.