The “is empty” option is available when targeting Sub ID or Carrier/ISP. It checks the query string in the ad tag for the selected Sub ID or the Carrier/ISP info to see if there is a value being passed to UpRival. If the query string is blank the “is empty” condition would be true and the ad would serve. If you have the Inverse Condition button checked, then the condition would be true if the Sub ID or ISP info were not empty, or in other words there is a value in the Sub ID or ISP query string.
A common use case for this would be if you are using a DSP and passing through the exchange name as Sub ID 1. Then setting up an ad group to display when Sub ID 1 is empty. This will allow you to track the impressions and clicks that are coming from anonymous exchanges or when the DSP fails to pass info through Sub ID 1 (i.e. during creative testing).