Speaker Break-In - What Physically Changes During Break-In To Enable Better Sound?

You're dealing with a mechanical device with moving components. It's a bit like a pair of new shoes. They're designed to flex and move, but that sure isn't how they come from the factory. 

I have no way to prove any of this, but I "believe" that after listening to my speakers for awhile, they sound better after 30-40 minutes or so than they did at the beginning.  Perhaps the drivers become more compliant (?) or warm up a bit.  Whatever it is, the sound seems to fill the room better, the stage opens up a bit more, and the music becomes more involving.  As for break-in of brand new speakers, the crossover certainly may undergo some changes, although one could argue that certain manufacturers do test runs of new units at the factory to rule out any problems before they ship them out.  But as it is with my present system, with the preamp and amp already in "standby" mode, I have to believe that it's probably the speakers that go through a warm-up period.

The capacitors, resistors, inductors, internal wire, solder joints and binding posts. Capacitors alone take up to 500 hours to sound their best.  

Like kosst_amojan said, the diaphragms of speakers are stiff "out of the box." In my experience, shipping in cold weather will make them stiffer (or reverse some of the break-in); and full-range drivers seem to require more break-in. Complete break-in for some drivers require many hours and even weeks and months depending on how much they are played.

Physically you get older!!  I think it is a combination of our getting in tune with the different sound and I am sure what grannyring pointed out. And I strongly feel my system which is solid state sounds better after about 20 minutes playing. Could be just me thinking that though and it is not really happening.