These courses seem to have been popular, perhaps because the teacher of these courses was there to back up and help the students.

back 在这里是动词，意思是"支持"或"作为后盾"。 up 是副词，常与动词搭配表示动作的完成或加强。 back up 是一个短语动词，意思是"支持"或"帮助"，指提供必要的援助或支持。