The amortized constant time complexity comes from amortized analysis. This kind of analysis is used when we want to evaluate the total complexity of a sequence of operations. The amortized sequence complexity represents the average cost of given operation in the analyzed sequence
Things that are amortized time:
From CP Handbook The time complexity of an algorithm is often easy to analyze just by examining the structure of the algorithm: what loops does the algorithm contain and how many times the loops are performed. However, sometimes a straightforward analysis does not give a true picture of the efficiency of the algorithm.
Amortized analysis can be used to analyze algorithms that contain operations whose time complexity varies. The idea is to estimate the total time used to all such operations during the execution of the algorithm, instead of focusing on individual operations.