[sobani]

To expand on @hansvm answer, an example would be a hash table.

Insertion is O(1) (constant time), most of the time.

But once in a while the collection will need to increase the size of the underlying array, which causes the entire table to be reorganized. That specific insertion will then be O(N) (where N is the size of table). The good news is that this reorganization happens only once every N insertions.

So amortized insertion is O(1), even if in the worst case it can be O(N). Depending on your use case you can hand wave the worst case away with "amortized it's constant time", or you can choose a tree instead, for a more predictable O(log N), or you could use some other mitigating tactic, like initializing your hash table with enough storage _for all use cases_ so you can guarantee O(1).