To burn bridges is to do something irreversible, to act in a way that destroys any chance of returning to the way things were. For example: "She has already burned his bridges with his previous employer by publicly criticizing their marketing policy." The idiom was originated in the late 1800s and is derived from the concept of burning down a bridge after crossing it throughout a military operation, leaving no option but to keep marching. In the olden times, during the war, soldiers would cross a waterbody and then burn the bridge or boats they had used to prevent retreat and halt the following enemy.

Source: The Idioms