Here are some commonly asked questions about this topic.
What is a scrum master?
The Scrum Master is a master of process and an empowerer of people as they focus on maximizing the impact of the development team. They support the team by removing obstacles and representing Scrum to the rest of the organization.
A servant leader puts others’ needs first. The Scrum Master provides the team with guidance and direction (where and why, but not what and how). This approach allows the team to work with a healthy level of autonomy and agency and ensures they have the mastery and purpose needed to do their work.
They act as a mirror helping the team see where they are and how things are going. The scrum master protects the team’s health by balancing the product owner’s drive to complete the product with the team's long-term effectiveness.
A scrum master can definitely be remote, but with a caveat. This situation works best when the whole team is distributed. The scrum master's effectiveness will decrease if the rest of the group is co-located and they are the only remote member.
Can one person be the Scrum Master for multiple teams?
This combo is possible, depending on the experience of the teams and the frequency of obstacles you need to help remove. I’ve been the scrum master for two brand new scrum teams simultaneously. It was a bit more work at first because so much teaching was going on, though it eventually leveled out once the teams learned their new rhythm.