Vein has two main meanings:

1. A blood vessel that carries blood back to your heart. While arteries carry bright red oxygen-rich blood away from your heart to your muscles and organs, veins bring darker blood back to the heart to pick up fresh oxygen from your lungs. You can sometimes see veins as bluish lines under the skin on your wrists or the back of your hands. When a nurse draws blood for a medical test, they use a needle to carefully collect blood from a vein in your arm.
2. A streak or band of different material running through rock or other substances. Miners search for veins of gold or silver running through mountains. You might notice veins of darker color running through marble countertops or limestone. Leaves have veins too: those branching lines that carry water and nutrients throughout the leaf.

The word can also describe a mood or style running through something, like a vein of humor in a serious story. When someone says they'll continue “in the same vein,” they mean they'll keep going in the same style or direction.