What exactly is "breaking in" on a new cartridge ?

I am breaking in a Ortofon 2M Black

Those (burn-in, break -in) are frightening expressions or phrases considering the fragile nature of the objects involved. In Europe we use the expressions 'play in' or 'warm-up'(time) which are obviously more adeqate for the purpose.

No.

New piston rings, new semi-auto handgun, etc., these
things need mechanical "wearing-in", so they loosen up and
operate with less friction.

What is happening to a brand new cartridge during it's
"break-in" period ? I do not mean "warming up" for
regular daily playing.

Noslepums, if you read my first response, I indicated that all moving parts within the cartridge need to wear in so that they move freely in interacting with each other. I only indicated that a "warm up" period seems to help for each session. But that was not in place of the "break in" period. There are elastimers that hold the coils and stylus
and they are more "stiff or ridgid" when new. So as the record plays those parts "limber up" to move more freely and establish a path of movement that it will assume each time it plays. I think you answered your own question with you last comment. Yes as a piston ring wears to fit the cylinder or the action in a gun wears to slide more easily, a cantilever to which the coils are mounted need to do the same. The suspension elastimers need to limber up to reduce resistance to movement and more accurately track the groove. It has to move not only up and down but side to side as well. An analogy offered is a blind man reading braille with a limber finger rather than a splinted stiff finger.
http://en.wikipedia.org/wiki/File:Moving_Coil_Cartridge.jpg
this cross section may give you an idea of the inner parts
involved that need to "break in".
actually maybe this is a better read.
http://shure.custhelp.com/app/answers/detail/a_id/4072/~/high-fidelity-phonograph-cartridge---technical-seminar

It would be interesting to see a graph indicating the progression of change in cantilever suspension elasticity (or stiffness) over time played. As the suspension is stressed from movement of the cantilever and as the suspension becomes less/more elastic with age, the response of the cantilever and stylus changes. The ability of the stylus to trace the groove laterally and vertically, the quality of pickup (cantilever vibration control) and degree of resonance damping are affected during this protracted "break-in" period. Thus, "break-in" is ongoing and continues until the cantilever assembly is either rebuilt/replaced or the cartridge is tossed in the trash.

But is the relationship linear or curvilinear? There may be some validity in the idea of "settling-in" if the relationship is curvilinear; the initial period of "break-in" may be a rapid progression until a plateau of relative stability is reached. If this is the case then there is merit in the idea of a cartridge needing to "settle-in" until it's optimal level of performance is reached. Depending on the type of cantilever suspension that period could take more or less time. And the stresses that the cantilever are put through (range of frequencies and dynamics) as vinyl is played will likely determine the "settling-in" period.

Regards,
Tom