The Daily Scrum is a 15 minute event held at the same time and place every working day of the Sprint. The Developers use it to inspect progress towards the Sprint Goal and to adapt the Sprint Backlog, and what comes out of it is an actionable plan for the next day of work.
That last phrase carries the whole event. A Daily Scrum that ends without anybody knowing what they will do differently has spent 15 minutes and produced nothing.
What the 15 minutes are protecting
Fifteen minutes is short enough that the event cannot become the work. The Daily Scrum surfaces problems, and solving them properly usually takes longer than the meeting has, so the discipline is to name the problem, agree who will carry it, and take the conversation outside. An event generous enough to solve everything it uncovers stops being a replan and becomes a working session that most of the team sits through without needing to be there.
The fixed time and place work the same way. Deciding when and where to meet is a small cost paid every day, and removing it leaves the Developers with one less thing to arrange.
Who it is for, and who runs it
The Daily Scrum is for the Developers, and it is theirs to run. They own the Sprint Backlog, so they are the only people who can adapt it, and the event exists to let them do that together rather than separately at their desks.
The Product Owner and the Scrum Master take part as Developers when they are actively working on Sprint Backlog items. Otherwise they hold no special position in the event. Others may attend, and what they may not do is turn the event into something delivered to them, because a group answering to an audience is reporting rather than replanning.
The Scrum Master ensures the event happens and stays inside its timebox, which is a service to the Developers rather than a claim on the event. Facilitating it is optional, and chairing it is not the Scrum Master's job.
What the 2020 Guide stopped prescribing
The three questions many people still recite are no longer part of Scrum. What did I do yesterday, what will I do today and what is in my way appeared in the 2017 Guide as an example, and treating them as a rule produced a round of individual updates addressed to whoever seemed most senior in the room.
The Developers may select whatever structure and techniques they want, provided the event stays focused on progress towards the Sprint Goal and produces an actionable plan for the next day. Walking the board, talking through the Sprint Goal, or something a team invented for itself all qualify. Nothing in Scrum requires the event to be held standing, requires every person to speak, or fixes it to the morning.
Where it goes wrong
The common failure is the status meeting, in which each Developer reports upward and nobody adapts anything. It is attractive because it looks orderly and hands a manager something to act on, and it quietly removes the reason the event exists.
The opposite failure is the event that runs long because the team starts solving the first problem it finds. Half the Developers then spend forty minutes on something that concerned two of them, which is the cost the timebox was there to prevent.
What it does not replace
Developers talk to each other throughout the day, and the Daily Scrum does not confine that to one slot. It also does not replace Sprint Planning, since the plan it adapts is the one Sprint Planning produced. Detailed design and problem solving conversations often follow immediately afterwards with only the people involved, which is common practice rather than a rule.