Context
A context is a "space" in Moodle. Together, they define the navigational structure of a Moodle site. A course can be a context, so can an activity, resource or block.
Role contexts
The context is combined with Role permissions to define a user's capabilities on any page in Moodle. In the context of a specific course, some users have the permissions of a student and others of a teacher. While in another course, the same users may be assigned different roles because they are in a different context.
In Moodle 1.7 and onward, a permission context can include an activity module or a block. Thus a course can have many contexts in its space. These might include lesson, assignment, forum and quiz modules and blocks.
It is possible to assign a user different permissions based upon a specific context. For example, a user might be given the role of "student" for a course but be given a teacher's role in the context of one specific forum. Or a user can be a teacher of one course and a student in another course.
What this means is that different Roles can apply depending on the page the User is in.
Before anyone logs in to the Moodle, sitting at the log in page, or public front page, depending how you have set your Moodle up, they should have the role of "Guest". It is possible to change this but be careful.
In Moodle, when anyone with a user name and password logs into the Moodle, they become an "Authenticated User". How they are authenticated is different from their Role.
For any number of reasons, you may want a Users to become "Students" while in the Front Page context. (Be careful here, read on below before assigning roles.)
When they click to go to a Category context, they revert to an "Authenticated User". Once there, their User Name is scanned and their permissions are calculated and if they have permissions, they can have sufficient rights to be a "Teacher" or a "Course Creator" or even an "Administrator" in that context.
Alternatively, they may not have those rights but when they click to go to a Course, they may have the rights to be an "Administrator", a "Course Creator", a "Teacher" or a "Student" in that Course context.
This does not mean they have any of those rights in any other page or Course as they will no longer be in the same context.
Overview
Moodle contexts in version 1.8:
(Source: Development:Roles#Context)
