A written warning is a unilateral declaration of intent. Its purpose is to inform the tenant that a certain behaviour, e.g. noise at night or constantly late payments, is considered to be in breach of the contract and is a disapproved behaviour. The written warning therefore has, as the word states itself, a warning function and is intended to create an opportunity to refrain from the disapproved behaviour.
Disregard of a written warning or repeated lease violations (breach of contract) can have serious legal consequences for those who do not take the warning seriously.
The warning is not to be confused with the normal reminder for late payment. While a warning is a request to refrain from an action, a reminder is a request for an action (e.g. to pay the monthly costs).