Ok, sure it doesn't have to be time...but in no way could it be probability or chicken nuggets. Neither of those two things can contain the 3 spacial dimensions.

Basically in order for something to be a new dimension it needs to be able to contain every X, Y, Z at any given point along its axis.  So for example, at any given point in time there exists every point in space.  So as a result any location is not accurately defined by just X, Y, Z but also requires T. 

I can illustrate this by saying "Meet me in Central Park NY City, at the yellow bench just inside the southeast entrance." which is an X, Y, Z coordinate.  To which you would probably reply "When?" which is your way of asking for the T coordinate.  Your question is valid because at every point in time there exists the space that is currently occupied by Central Park.  So I might answer your question with "Tomorrow at noon". In any case all of this information gives you the exact location in space-time we are to meet which is defined by the coordinate quadruplet (X, Y, Z, T).