What is "Testing"?

Let's think of this as "one from the mailbag".  It comes up a lot on community sites and message boards, via email, in my workshops:

What does "testing" mean?  I see it referred to a lot in reference to fashion shoots and I'm a little confused.

One caveat: my answer is in the context of a major industry market (New York City, in my case) and may not apply the same way in smaller and local markets.  In general, the major markets (NYC, LA, Chicago, Miami...London, Paris, Milan, Tokyo, Shanghai) all behave in the same way...but all bets are off in the smaller markets, where every agency and client and photographer is reinventing the wheel.

Let me start with what "testing" doesn't mean:

It doesn't mean "I'm shooting a proof-of-concept for a commercial/client project and I'm going to use a model to stand in for it so I can try out a technique and show the results to my client before we pay the real talent."

It doesn't mean "come stand in for me while I test out new equipment."

It doesn't mean "a model agency is going to have a model do a dry-run photo shoot in order to decide whether he/she is worth signing."

It doesn't mean "you're going to model for me for free for a quick shoot in order for me to decide whether you're worth paying to model for a longer shoot."

So what does it mean?