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

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

In addition to what Bill stated, IMHO, the mechanical side, (spiders, surrounds, voice-coils, etc.)  is just as important to break-in.

Nothing changes *physically*. What changes is your ears and perception. Try the same thing with second hand speakers. You'll swear they too are breaking in. Balderdash.  If the compliance of all mechanical parts "broke in" over several hundred hours, that *degradation* in materials would not magically stop at the precise point at which they magically reach their best sound.  It's not magic, it's accommodation <erects flameguard>.

Two key factor's regarding break-in why one should wait 60 to 100 hours.
If you purchased a truly high end 3-way floor stander, where the crossover is on three separate boards, combined with very exotic drivers, then more time is needed for burn-in for the crossovers. The piston's in a new mid-range and woofer are somewhat stiff and should be broken in slowly to avoid off center piston alignment, and play at low volume for at least 60 hours for the piston's to break in to maintain perfect alignment.
If you take a brand new high end speaker right out of the box and crank it at full volume for an extended time, bad mistake. You could permanently throw your piston's out of alignment that could impact the quality of sound especially from the woofer. 

I’m inclined to believe that the thing that’s changing is ourselves i.e. we are becoming accustomed to the sound of a new and unfamiliar device, rather than anything "burning in", or whatever.