The roles and responsibilities of the Scrum Master may vary based on the distribution environment and team structure, but there is always a component that seems to be common for all cases, and this is ensuring that the team is following Agile practices. It becomes imperative in the distributed environment since most of those practices were initially designed for the collocated teams. As a Scrum Master, she/he is responsible for coaching the team and helping them overcome those challenges.
Distributed teams can adopt not all Agile practices; some have to be significantly modified, and some will require specific tools, which means that the team will have to invest in some learning time to adopt them. One of the classic examples of those modifications is pair programming. In distributed Agile environments, pair programming is replaced with code reviews. (Personally, I have found code reviews more efficient that pair programming even within the collocated teams).
Another practice that is critical in a distributed environment is continuous integration which will ensure that everybody is working on the same code. The implementation of this practice can be challenging from the technical point of view but is well worth the investment. It also requires that all team members understand the importance of daily code check in, even though the particular feature they are working on may not be finished. If the code is throwing exceptions or prohibiting any previous functionality from testing, it should be commented out, but still checked in. The Scrum master is responsible for communicating the importance of Agile practices to all team members.
One of the other Scrum master responsibilities usually includes tracking iteration progress. In collocated environments. Iteration tracking is visualized by sticky notes on a wall so that every team member can see the current status of the particular issue, and update the status on items assigned to him during the daily standup meeting. In distributed environment, you need to use something more advanced to visualize the progress. There are fairly large numbers of tools available today in the market which do an excellent job of visualizing iteration tasks, keeping track of backlog items, and generating burn down charts.
This is an excerpt from the forthcoming book, The Art of Being Agile.