what does it really mean?

It's a figure of speech referring to a person who has become very sad. Relationships end, pets die, family members die, love is lost....

only ego can break and only ego can feel pain ! - only ego-heart can become "broken heart" a broken heart hence only means you have ego and part of your ego is causing pain to YOU and/or others ! the pain you feel is the pain you cause to others ... ego either is dissolved by YOUR TRUE love for GOD AND ALL or breaks into pieces to free you on the path of pain the choice of path - love or pain - love or karma - always is yours a truly and divinely loving heart only loves ... - hence never fears rejection or attraction - never fears oneness or separation a truly loving heart just loves ... - in union as much in separation from the beloved one .. - in darkness as much as amidst loving ones .. - in heaven as much as in hell - a truly loving heart ALWAYS loves - anywhere and everywhere and ALL ! loves eternally - for ever and ever and infinitely !

When I get a broken heart, I can actually feel a hurt feeling in my chest. I feel saddened and my feelings hurt.

It means you're in a lot of pain from sadness. Someone who cared about deeply has hurt you emotionally.