Good morning, child.
That's a fair and thoughtful question. There's a cool and slightly-scary term that you'd want to understand first: self-abnegation. Both genetics and experience teach us the importance of a strong self so that we can practice self-protection, self-defense, self-preservation. Those are guides and shields that can, over time, turn into ruts and shells. They leave us safe but barely alive, barely capable of experiencing anything new because "new" is risky. Self-abnegation surrenders ("negates") the self and, in doing so, frees it.
The impulse to self-defense is controlled by an ancient and very powerful part of the brain, the amygdala. It's a little almond-shaped organ (hence the name, from the Latin for "almond") at the back of your brain and it is very twitchy. Anything that might conceivably represent a threat (think "radical change in diet") is quite enough to trigger its panic reaction, which we sometimes term "fight or flight." If a strange dog lunges at you (even a hologram or a 3D movie dog), there's no amount of thinking that can get you to hold still - the amygdala simply short-circuits the message from your sensory organs to your cerebellum: "let's think about this" is simply not an option because the amygdala has triggered a different reaction first.
It is possible to sort of anesthetize the amygdala, to put it into sleep mode while allowing the more advanced part of the brain to run the show.
"Breaking" is the process of eliminating a sub's ability to pursue self-interest, self-protection, self-preservation, self-defense. It might be achieved quickly by imposition of force majeure: once the shackles and gag are in place, you no longer have the ability to protect yourself in any way (the toy goes where your Dom/me wants it to go, the lash lands where and when S/He wishes, the pictures go where S/He wants them to go). In theory, you could be broken in a single, long exhausting session. And, in theory, the breaking is followed by liberation: when I say "unbutton," you don't question. You don't worry. You don't hesitate. You unbutton and experience.
The breaking process is, by turns, inconceivable, terrifying, hard, scary, tough, frightening. In practice, especially given the constraints of computer-mediation, breaking is a more gradual but still relentless process. Every day you take one step forward; the doors behind you, your avenues of retreat, are not slammed shut but are slowly closed. As you're led, more and more of your identity becomes tied to Him (or Her). More and more, the thought of disappointing Him - the thought of losing Him, even briefly - becomes frightening, then terrifying, finally inconceivable. At base, your amygdala is surrendered to his service.
Doubtful? You might pose the following hypothetical to your sisters: "You were given a rule. You were thoughtless and clearly violated it. S/He's angry and you're ordered to choose your punishment: you will be beaten with a belt to the point you think you're losing your mind or you will be completely cut-off from your Master for the weekend. Grounded. No email, no chat, no chat, no looking at His picture, no speaking His name, no wearing your collar, no log-in to your shared account. Just 48 hours to reflect. Which would you choose and how long would it take you to decide?" A broken girl would, I suspect, not hesitate in her answer.
Unfortunately, many Dom/mes are human. Flawed, irresolute, unreflective, subject to whim and distraction, inconstant. As a result, they botch the process and leave the sub dangling. (Which pisses me off, but that's a separate rant.)
I'm not sure if that's exactly a universal understanding of the term but it is (a) mine and (b) probably in the commonly-understood direction, give or take some fine-tuning by others wiser than me.
Hope that helps,
Solis