1. Gets you out of a desperate mindset
First thing after a breakup, you're feeling desperate and crazy. "I've got to get her back. She'll forget me if I don't beg her to take me back." Thoughts like that go through your mind and become very difficult to deal with.
Unfortunately these are also the EXACT OPPOSITE of the thoughts we should be having, which are:
1. My life is okay without my ex.
2. I will be fine without her.
3. Now is my chance to recover and get my life in order.
4. I can always get her back later; it's not the end.
But not many of us think that way after a breakup. So this is why the no contact rule works so well; it gets you out of that "crazy mode" post-breakup.
2. Allows you to heal
Another great thing about going no contact is that it lets you heal from the wounds of your relationship. Maybe you've been in a relationship with your ex for many years; surely you've said and done things, and they've said and done things, that you would rather forget.
Now you can examine each aspect of your relationship intently. Was it actually as rosy as you're painting it out to be? Often, just the panic and desperation that comes from perceiving that we've lost someone make us think it was much better than it actually was, as far as a relationship goes.
3. Lets you approach your ex in a calm state
Finally, the no contact rule works because it allows you to finally approach your ex, when you re-establish contact, in a calm state of mind. This is MUCH better than madly texting her after she's broken up with you. That is going to backfire.
Instead, you can re-establish contact after 30 days of no contact and casually ask how she's doing or something along those lines. You want to be very careful what you say at this point of reconnecting; you DON'T want to talk about the breakup with her.
In a way, you're getting a totally clean slate, a fresh start. You have to approach her from a different angle, where the past is in the past, and now your focus is just on being friends. Any relationship stuff is way down the road, and should not be the primary goal on your mind.