Andrew Everard:
Some use tends to loosen up the mechanical components of speakers, not least the surrounds on drivers, which soften a little with some flexing back and forth.
The results can be better bass control and definition, and a slight softening of overbright treble, though the degree of change tends to vary from speaker to speaker, and dependent on other factors such as ambient temperature, humidity, driver and suspension materials, etc...
The one thing that can be said about all five pairs of speakers that I have owned from new is that they sounded no worse after running in. With the first two speakers my amplifier was so bad that no running in was detectable. The other three became less mechanical and more musical. Notably, my Wharfedale Valdus 100SEs sounded bassy, muffled and monochromatic when new but they changed more during running in than any of my other speakers, developing an open, colourful and musical sound.