A CyclicBarrier is cyclic because it can be reused without resetting. From the Javadoc
A synchronization aid that allows a set of threads to all wait for
  each other to reach a common barrier point. CyclicBarriers are useful
  in programs involving a fixed sized party of threads that must
  occasionally wait for each other. The barrier is called cyclic because
  it can be re-used after the waiting threads are released.
So in normal usage, once all the threads are collected and the barrier is broken, it resets itself and can be used again.
From the Javadoc for reset()
Resets the barrier to its initial state. If any parties are currently
  waiting at the barrier, they will return with a
  BrokenBarrierException. Note that resets after a breakage has occurred
  for other reasons can be complicated to carry out; threads need to
  re-synchronize in some other way, and choose one to perform the reset.
  It may be preferable to instead create a new barrier for subsequent
  use.
So reset causes any currently waiting threads to throw a BrokenBarrierException and wake immediately. reset is used when you want to "break" the barrier.
Note also the caveat - once the threads have been awoken forcibly it's tricky to synchronize them again.
TL;DR: you should never need to use reset() in normal circumstances.