Amortized time complexity

#1

what is amortized time complexity?? Please simplify this

#2

Amortized complexity is the total expense per operation, evaluated over a sequence of operations.
Example:
The behavior of C++ std::vector<> . When push_back() increases the vector size above its pre-allocated value, it doubles the allocated length.

So a single push_back() may take O(N) time to execute (as the contents of the array are copied to the new memory allocation).

However, because the size of the allocation was doubled, the next N-1 calls to push_back() will each take O(1) time to execute. So, the total of N operations will still take O(N) time; thereby giving push_back() an amortized cost of O(1) per operation.