Figurative expression for tears shed in extreme grief, anguish, or hardship. The literal meaning 'tears of blood' is also understood but the phrase is almost always used figuratively.
He parted from his family with bitter tears.
Hearing that story, I was so sad I could have wept tears of blood.
Compound of 血 (chi, 'blood') + の (no, possessive particle) + 涙 (namida, 'tears'). The figurative use is ancient and appears in classical literature.