Broken blood vessels are enlarged or dilated blood vessels beneath the skin's surface, appearing as pink or blue spidery lines usually on the nose, cheeks, legs, and face. Often called "spider veins", you may also have these in any other part of the body.
While visible blood vessels or dilated capillaries are harmless, patients may have them treated for better blood flow and a clearer, smoother appearance of the skin.
Cited from the Mayo Clinic & the American Academy of Dermatology