To adapt a new lifestyle which is in stark contrast to the one you previously had. Generally used when someone who previously followed rules and regulations begins to deviate from them to achieve new goals/desires. The term is most often used when someone who is generally accepted as "good" adapts behaviors which are seen as "bad".
"What he's just gonna break bad?” Jesse Season 1, Episode 1 Breaking Bad
"Walt broke bad when he was diagnosed with cancer...."
similar to "crack wise" from an earlier era, except that where one who cracks wise is at most sarcastic and disrespectful (and may be just funnin' in genuine good humor), one who breaks bad has escalated to being combative, belligerent, or threatening; while not excluded, there need be no humor, attempted humor, or affected humor involved when a person breaks bad, again by contrast to cracking wise.
"Joe was talking shit to Ted, and it actually was kinda funny, but then Ted broke bad and started gettin' up in Joe's face. For a little bit, I thought they were maybe going to really mix it up."