1.Someone who feels too much sympathy for people such as poor people or criminals etc.
2.someone, usually considered politically liberal or leftist, who is very emotional about certain political issues, such as endangered species, downtrodden people, the suffering poor, etc.
The man is a bleeding heart and he is always asked by other people for money to help the victims of flood.
Sanjay is such a bleeding heart. He always help his poor classmates.