The groups field on student records is an optional field. When provided it allows teachers to filter specific sets of students in the student search by their group name.
Typically schools use the students grade level as their group. Alternately is can be convenient if students only have a single teacher to use the teacher's class name as the group.
Students can belong only to a single group.
TIP: If your school uses ClassLink sync with the Groups option enabled. Sync will set each students Group to their Grade Level as it exists in ClassLink.