table in database

Student (with a capital S) is the class that provides a 1:1 mapping to database with the Model class that was imported with Peewee. So, yes, it is essentially a table. Not calling it "Students" is more of a python convention, which states that this class should always be singular. The documentation for peewee wasn't too clear on why this was, but I would guess it has to do with the fact that this class just describes how the data should be added to the database. It hasn't actually added any students to the database yet.

students (plural and lowercase) is the dictionary list that contains some initial students. However, these students have not been added to the database yet. The add_students function will do this with the the following for loop:

def add_students():
    for student in students:
        try:
            Student.create(username=student['username'],
                           points=student['points'])
        except IntegrityError:
            student_record = Student.get(username=student['username'])
            student_record.points = student['points']
            student_record.save()

In this case, the for loop is saying to loop through the "students" list, create an instance of Student, and add it to the database. You could use something besides a lowercase, singular "student" (e.g. person) in the for loop. This just makes it a little more clear on what it is doing.