The Definition of Done is crucial in Scrum because it ensures a shared understanding among all team members about what constitutes a completed Product Backlog item. This shared understanding is essential for maintaining transparency, which is one of the core principles of Scrum. When everyone understands and adheres to the Definition of Done, it prevents any ambiguity about the quality and completeness of the work.
Furthermore, having an agreed and transparent Definition of Done allows the Developers to accurately Forecast the work they can complete within a Sprint. It also facilitates the inspection of the Increment and the Product Backlog during the Sprint Review, as everyone can clearly see which work is Done and which is not.