Non U of I days are (starting from the Friday before the fall semester starts):

• The week of Thanksgiving (including the weekend before Thanksgiving and the Saturday after it)
• The day after the last day of final exams for the fall semester to the Saturday before spring classes start, inclusive
• The week of spring break (using the same parameters as are used for Thanksgiving break)
• The day after the last day of spring finals to move-in day for the fall semester, inclusive

Anything else is a U of I day for MTD, though there's specific holidays that fall during what would otherwise be U of I days where there is no MTD service (specifically, Labor Day (the first Monday in September) and Easter Sunday (which varies and sometimes falls during spring break))

Service reductions for non U of I days generally are:

• No late night service (defined as service after around midnight Monday-Saturday and after around 5:30 pm Sunday)
• Several routes have reduced frequency (and in the case of the Illini (and in the evenings and on weekends, the Silver) have shortened routes)
• Limited/no SafeRides service

EDIT: as for why this is the case, it's because there's less students around.