You can use ‘break out’ when you are talking about the beginning or start of something big, such as war, a social movement or disease. To ‘break out’ can also mean 'to escape’ from somewhere or something, such as prison, a way of life, or an unpleasant or restricted situation. To ‘break out’ can refer to spots or a rash spreading on the skin, usually caused by illness or an allergy. To ‘break something out’ can mean ‘to launch something’ or promote something to the public, such as a new product or service.
Additional examples with 'break out' are:
You describe to your friend the film you went to see at the cinema last night: "The film was about two criminals who managed to break out of a high-security prison."
Two political party leaders became involved in a heated argument: "An argument began to break out between the two leading parties during the debate."
A colleague has been going through a difficult time in their personal and professional life, and they feel stuck in a negative way of thinking: "I need to find a way to break out of the negative mindset I am in at the moment."