There are two ways of looking at student activity on an assignment. The first way is to look at overall student activity on the assignment. The second way is to look at one particular student's activity on the assignment. The first method is the macro level, while the second is the micro level.
Looking at the Overall Student Activity on an Assignment
From within the Gradebook, click on the assignment you would like more information on (in this case QUIZ 1).
Once within the assignment, you can scroll down to access all of the overall student metrics for the assignment. You can see the Frequency of Scores, Frequency of Grades, Submissions and Question Difficulty/Discrimination.
Looking at One Particular Student's Activity on an Assignment
Then click on the particular student in question on the left (in this case, "Five, Student").
You can then see the particular student's responses to each of the questions in the assignment. From this screen, you can also alter a student's grade on the assignment, provide feedback to the student or yourself, excuse the student from the assignment (an excuse puts an "x" in place of a grade) and allow the student to have a retry (a retry gives a student a second chance, but does not allow you to add a due date and time).