If you describe someone as a bleeding heart, you are criticizing them for being sympathetic towards people who are poor and suffering, without doing anything practical to help.
[disapproval]
I'm not a bleeding heart liberal.
bleeding heart in British English
noun
1.
any of several plants of the genus Dicentra, esp the widely cultivated Japanese species D. spectabilis, which has finely divided leaves and heart-shaped nodding pink flowers: family Fumariaceae
2. informal
a.
a person who is excessively softhearted
b.
(as modifier)
a bleeding-heart liberal
bleeding heart in American English
1.
any of several dicentras, esp. a common garden perennial (Dicentra spectabilis) with racemes of drooping, deep-pink, heart-shaped flowers
2.
a person regarded as too sentimental or too liberal in dealing with social problems
Examples of 'bleeding heart' in a sentence
bleeding heart
A bleeding heart in a pink silk shirt, Schumacher muttered to himself disdainfully.
Dobbs, Michael WALL GAMES (2002)
Sails were set under a dazzling crimson sun the superstitious crews on both ships solemnly described as red as a bleeding heart.