The Scrum Master's primary responsibilities are to guide the team in creating and following its own process (e.g., the Scrum framework) and to enable and drive them to meet their commitments. The Scrum Master understands that successful sprints and releases build trust within the team and across departments and that an individual's senses of mastery, purpose, and autonomy drive their intrinsic motivation to improve performance and lead to greater overall satisfaction and self-identification with organizational goals.
The values, artifacts, practices, and roles of the chosen agile methodology.
Act as Agile Coach to the team and organization.
Removing impediments. The Scrum Master helps the team raise issues and removes the blockers that prevent progress.
Protecting the team from interruptions to the sprint commitments (including new work, unrelated meetings, and non-Scrum reports).
Making progress visible. The Scrum Master helps the team to update their status and "hours remaining" on tasks and ensure the team area has a BVIR (big, visible information radiator) to indicate progress and quality.
Acting as "chief communicator". The Scrum Master shares information about the team's work with others as needed, and ensures that relevant information gets in.
Owning and enforcing the agile process. The Scrum Master helps the team to understand how agile practices support good work, helps the team adapt those practices without losing the disciplines and benefits that bring value.
Facilitating team decision-making. A good Scrum Master doesn't make decisions for the team but establishes practices that support and coaches the team to make good decisions. This includes ...
Helping team establish working agreements.
Hosting and managing parking lots during meetings.
Encouraging that egos and roles be left at the door.
Managing conflict (including the natural tension between the delivery team and the product owner) and asking the team to work together in new ways.
Facilitating agile maturity by modeling the agile values and the behavior they want from the team, coaching the team on agile behavior and skills, enforcing agile values and practices, and reminding and encouraging the team to hold each other accountable to these values and to their working agreements.
The Scrum Master does not make decisions for the team. (Remember: The team is self-organizing.)
Web page: "Scrum Master Checklist" by Michael James.
Book [paid]: "Collaboration Explained: Facilitation Skills for Software Project Leaders" by Jean Tabaka