As a scrum master I have asked a question many times (even by myself) to provide a clear picture of what a Scrum Master really does. To help myself and others, I have started writing down the responsibilities of the Scrum Master.
1. As a Scrum Master he/she must make sure Scrum process is followed
2. Scrum Master should help to organize meetings (i.e. stand up meetings, scrum of scrum meetings)
3. Scrum Master should be full time facilitator for the team
4. Scrum Master should enforce time box
5. Scrum Master should make sure back log items for the upcoming sprint are prioritized by the product owner and ready for the sprint planning meeting.
6. Scrum Master should help the team to focus on current sprint to achieve the sprint goals
7. Scrum Master should make every effort to develop a team into high performance team
8. Scrum Master should encourage team members to be self-organized
9. Scrum Maser should support team building/team development by utilizing the abilities and skills of individuals, and developing a feedback culture
10. Scrum Master addresses team needs efficiently and effectively
11. Scrum Master has to work with the team/organization to solve impediments
12. Scrum Master should work with product owner and make sure the team has the cross functional team members (i.e. development, testing, UI designer, documentation)
13. Scrum Master has to identify the solve the hidden problems with the team members
14. Scrum Master has to educate and focus the team towards business driven development
15. Scrum Master has to make sure the feedback given during the sprint review meetings are captured by the team members and help the team members to learn from the experiences