What does a broken blood vessel in the eye mean?

Usually nothing: Sub conjunctival hemorrhage is a common condition. It may be due to blood pressure ore eye pressure. But usually a cause is not found. Any valsalva maneuver may cause a capillary to break, even heavy lifting or constipation. It is usually benign. But have your eyes checked.

Usually not much: It can come from coughing, sneezing, constipation, airborne irritants hitting the eye, a mascara wand, or even hitting the eye during sleep with a blanket or pillow edge. All bets are off if on blood thinners.