Special student Harvard in Mathematics
You need to check on the rules at Harvard, but in general, "special student" generally means that a student is allowed to take courses but not to get a degree from the university.  The phrase "non-degree seeking student" is also sometimes used for this status.  

It can be easier to be admitted as a special student than as a regular student, but it's also typically hard (as hard as getting admitted as a regular student) to switch from "special" status to regular degree seeking status.