"Break your heart" is an English idiom describing someone who has been made extremely sad or upset by someone or something else. The most common usage of this idiom comes in terms of romantic relationships that have ended badly for one person involved. In addition, people may use the phrase on occasions when no romance is involved, especially if they are deeply saddened by some occurrence. This phrase gets its meaning from the fact the heart is often considered to be the organ in the human body which contains feelings of love.
There are often many different ways that a person has at his or her disposal to say essentially the same thing. While it would be fine to simply use the actual words which mean what they want to convey, there are times when more colorful and impactful language can be more effective. As examples of this type of language, idioms are phrases which gain meaning that can be far separate from the literal meaning of the words they contain. Popular usage of these phrases within a culture gives idioms their accepted meanings. "Break your heart" is one of the most popular idioms used to describe a romantic calamity.
Obviously, someone who literally has a broken heart would have severe medical issues. That severity is where the idiom gets its powerful meaning. As an example of how it is used, imagine someone who says, "If she leaves you after all this time you've spent together, it will really break your heart."
Of course, there are many occasions which call for this idiom to be used, even if there is no relationship ending. For example, a death in the family can leave someone with a "broken heart." The usage of the expression has been stretched out so that is used in far less serious situations. In this vein, it wouldn't be unlikely for a sports fan to say, "You shouldn't ever expect that team to win the championship; they'll only break your heart in the end."
Since the phrase is romantic in nature, it is a very popular idiom for both poetry and song. Both of these methods of artistic expression often tend toward exaggerated, colorful expressions necessary to convey deep emotions. As such, "break your heart" is particularly suitable for those occasions. The idiom has become one of the most popular idioms in the entire English language, especially when the similar idiom "broken heart" is also taken into consideration.