It means to gain freedom from something that was confining you or holding you back. It can be used literally as well as applied to abstract objects or ideas.
"He was very troubled by the past events, but when his sister came requesting his help he broke free from his troubles and moved forward."
"As a child she was limited by her handicaps, but as she grew into adulthood she broke free from their bonds through sheer determination."
"The zoo was evacuated when the officials noticed the lions breaking free from captivity."