An Interval simply means a unit of time. In this case, as timeshares are generally sold in one-week shares, Intervals generally refer to a period of 7 days. For example, one week of timeshare ownership is an interval week. An interval week will usually be assigned a week number, based on a timeshare calender, depending on where in the year it falls. An Interval, or calender week shows and numbers the 52 or 53 weeks in a year, emphasizing the check-in dates on which each Interval week begins (Friday-Friday, Saturday-Saturday or Sunday-Sunday.)
The exchange company Interval International, likely gleaned its name from this term- as it allows owners to trade their time (or Interval) at one in-network resort for time at another.