How can a rubric help a student meet their teacher's expectations for an assignment?
A rubric can help your students to understand your expectations for an assignment because it tells exactly what you are looking for on that assignment and how important each aspect of the assignment is.
Without a rubric, students may be unclear as to what you, the teacher, want. If you just tell them, for example, to write a good essay, they may not know what you mean. But if you create a rubric, they know exactly what you mean by a "good essay." They know how much weight you give to things like grammar and spelling. They know how many sources you expect them to cite. They know all of the criteria on which they will be graded.
Thus, using a rubric can help your students understand what you want, thus helping them to get better grades.