This Post (including the links below) concerns standard 6-sided dice.
One might think of various extensions of the concept that follows and then deal with other types of dice. But for the moment, we restrict ourselves to normal dice with 6 faces, numbered from 1 to 6.
When rolling two dice, it is common (in hundreds of games) to look at the sum of the numbers shown (on the upper surfaces of the dice). As you know, there are 11 possible results (from 2 to 12) from a roll with 2 dice.
The new idea is to look at the sum of the numbers not shown on any dice. In that way, we get 11 different possible results (namely the numbers from 10 to 20, i.e. with two dice).
The name inverted dice was chosen for this way of interpreting a roll of dice.
Some examples are required, see the links below. Also, see the rules.