It means you got angry or emotionally upset very fast ... almost in an instant .. because someone or something irritated or bothered you with something they said or did. Example. I was very tired and restless, and had been trying to sleep for hours in bed. My nerves were on an edge - I was very irritable. Suddenly, the phone rang and suddenly "something in me snapped". I couldn't take it any more, I got angry and jumped out of bed and was very rude to the person calling me on the phone.

You lost connection with an internal source of discipline or control

“Something in me just snapped” and “I just snapped” are very similar. The first conveys a slight sense of being less responsible or less capable of understanding what happened.