<p>What is meant by "Constant Amortized Time" when talking about time complexity of an algorithm?</p>

It means that over time, the worst case scenario will default to O(1), or constant time. A common example is the dynamic array. If we have already allocated memory for a new entry, adding it will be O(1). If we haven't allocated it we will do so by allocating, say, twice the current amount. This particular insertion will
not
be O(1), but rather something else.
What is important is that the algorithm guarantees that after a sequence of operations the expensive operations will be amortised and thereby rendering the entire operation O(1).
Or in more strict terms,
There is a constant c, such that for
every
sequence of operations (also one ending with a costly operation) of
  length L, the time is not greater than
  c*L (Thanks
Rafał Dowgird
)