Grading student's assignments is only part of the Grade Center.  Another part is adding comments, letting students know why they lost points or where they could find additional resources to help with the course.

From the "Needs Grading" window, you can click on the small speech bubble above the assignment preview or type in the "Feedback to Learning" box to leave comments and notations for your students .

From the "Full Grade Center" window, you can also click on the small gray arrow by each assignment grade and select "Quick Comment" to leave feedback for your student.