A written warning (Abmahnung) is a formal request to stop doing something. It’s usually the last warning before suing someone. It gives the person a chance to fix the problem without going to court.
A written warning can also ask the person for money. For example, “you used my photos without permission; give me 500€ or I will sue you”. You can refuse to pay or negotiate a lower price. If you can’t find a solution, the person who sent the warning can sue you.
An Abmahnung is similar to a cease and desist letter, a letter of demand or a mise en demeure in other countries.