This is just the reputation that the user has earned for the given period (day/week/month/quarter/year).
For example, for you, for Stack Overflow, the API currently returns:
"reputation_change_day": 0,
"reputation_change_week": 0,
"reputation_change_month": 32,
"reputation_change_quarter": 63,
"reputation_change_year": 111,
This should jibe with what you currently see on your "multi-super-whatever-you-call-them drop down".
It matches what we see on the Users page, reputation tabthe Users page, reputation tab:
And what we see in [the Reputation Leagues][6] :
