“The Scrum Master enforces the rule that only Development Team members participate in the Daily Scrum.” – The Scrum Guide.
What does this mean and why is it important?
The Daily Scrum is a meeting for the Dev Team, in which they can inspect progress towards the Sprint Goal and adapt accordingly. This means that only dev team members participate in a focused discussion concerning their work (e.g. by answering the three questions). This is their responsibility and they know best how to do it. The daily is for the dev team and serves no other goals, such as status updates for others.
By helping others respecting the daily by NOT participating, the dev team can be completely transparent and open in the meeting, yielding to them the best results.
By helping others respecting the daily by NOT participating, the dev team be focused on what is needed (or is blocking them) for focused sprint execution towards their goal.
That being said, I often find it useful if the PO is present at the daily, and often find that the dev team aligns with the PO quickly during the daily. It is also a good moment for the PO to ask the team some minor questions or align wrt meetings with customers or users requiring involvement of the Dev Team. But strictly speaking this should not be part of the daily scrum. —