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.
その話を聞いて、血の涙が出るほど悲しかった。
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.