What is "Excess Supply"?What is an excess function?

Over and over and over, we hammer into our introductory economics students that a change in price causes a change in the quantity supplied. "Quantity supplied" is a function of price (and a host of other variables), and we refer to this function as "supply". In other words,

Supply is a function, not a quantity.

So how is it possible to have an "excess supply"? What on earth is an excess function? I really doubt that most people mean some sort of excess supply function when they say "excess supply".

What we really mean is, "an excess quantity supplied at a given price [which is above the market-clearing price]." And yet, I don't know of any textbooks (other than my own) that talk about it this way.