What is an auxiliary assumption?

The word "auxiliary" in this context means "supplemental" or "supporting", because the assumption that is made supports the given hypothesis (or explanation) but is not actually part of it.  We do this all the time.  Think about this example:

When someone predicts that a certain sports team will win a particular game by so many points, that person is assuming:  (1) both teams will have their normal starting players available for the game, and (2) both teams will play as well (or as poorly) as they have in the recent past.  If either of those two auxiliary assumptions is false, then the prediction about the outcome of the game is unlikely to be accurate.
    

In the realm of natural science, we also make auxiliary assumptions.  For example, when scientists attempt to discover physical "laws" governing the Universe, they assume that such laws exist!  Geologists are especially prone to making auxiliary assumptions, because we often interpret geologic history based on what we understand about present-day geologic processes: but how do we know that these processes occurred at the same rates and in the same ways during the pre-historic past?  We don't, we assume that this is true!