From Latin 'vena' (blood vessel, water channel, mineral lode, streak of talent) — all meanings passed to English.
A blood vessel that carries blood toward the heart; also a thin layer of mineral or rock in a fissure, or a distinctive quality or style.
From Old French 'veine,' from Latin 'vēna' (blood vessel, vein; also a water channel, a mineral lode, a vein of talent). The Latin word is of uncertain deeper origin — no secure PIE etymology has been established. Some scholars have proposed a connection to 'vehere' (to carry, to convey), from PIE *weǵh- (to carry, to transport), since veins carry blood, but this is speculative. The word's multiple meanings in Latin — anatomical, geological, and figurative — all passed into English
Latin 'vēna' carried the same triple meaning that English 'vein' preserves: a blood vessel, a seam of ore in rock, and a streak of talent or temperament. Romans would say someone had a 'vēna' for poetry — a natural current of ability running through them — just as English speakers say something is written 'in a humorous vein.'