It's a more informal and exaggerated way of saying "very happy" or "overjoyed."
Here are some examples of how it might be used:
* "I was chuffed to bits when I got the job offer."
* "She was chuffed to bits with her birthday presents."
* "They were chuffed to bits that their team won the championship."
Essentially, someone who is "chuffed to bits" is experiencing a high level of happiness and excitement.