For example, it is the difference between viewing the possible results of rolling a six sided dice as {1,2,3,4,5,6} rather than {6, not 6}.
One way to think about this is that some people consider the set of possible outcomes for rolling a six-sided dice to be {1,2,3,4,5,6}, while others exclude the possibility of rolling a six, effectively considering it as {6, not 6}.