Teacher is one of the three core user roles in Moodle. The others are Administrator and Student. These roles have privilages and control what you can and can't do within particular areas of a Moodle. In short, an Administrator can do almost anything and go anywhere, a Teacher has control over a specifc course within a Moodle and the experience of the learners, and a Student participates in a course.
The term 'Teacher' can be changed to something else in the course settings or in the site settings. For example 'Tutor', 'Facilitator', 'Professor' or 'Instructor' might be more appropriate. The default term is Teacher and is generally used throughout Moodle documentation.
A participant/user is assigned the 'Teacher' role in a specific course. Being a 'Teacher' in one course does not give you any special privilages in another. For example, you must be specifically added to a course as a 'Teacher', or a 'Student', or be allowed in as a guest to have any access at all.
In later versions of Moodle, the role of teacher has been further defined. There is now a role called course creator. This role can create a course, assign Teachers, plus have all the privilages of a Teacher. And there are teachers who can edit content and teachers who can not edit. The non editing teacher roles are view as mentors or course adjuncts.
Clicking on the "Teacher" link below will take you to the same place.