An idempotent operation can be understood as something that establishes a value or state instead of modifying it.
A simple example might be the bank balance. Imagine the extract below:
Data Valor Operação
01/01/2017 100,00 Abertura de conta + Depósito inicial
02/01/2017 -14,99 Netflix
03/01/2017 -20,00 Refeição
04/01/2017 -30,00 Táxi
01/02/2017 5,01 Saldo Atual
02/02/2017 +14,99 Extorno - Netflix
If you want to know the balance of this account on 06/01/2007 you can not only observe the last amount processed, because it is a modifier (-30 reais on 1/4) . You need to consider all modifications until you find the first value defined by an idempotent operation - in this case, the account opening with the value of 100 reais.
The message on 01/02 can also be considered an idempotent operation: Many systems use this mechanism to facilitate state assessments. In the example above you do not need to recalculate all values until the first operation to determine the current balance.