The tall container you put flowers in is a vase. Thanks for the enormous bouquet of daisies — I'll need to find a large enough vase to fit them in!
A vase is a glass or ceramic container that serves only a decorative function — in other words, you're unlikely to serve a guest a big glass of lemonade in a vase. Vases are generally tall and narrow, to accommodate flower stems. Some vases are curvy and others are straight. In North America, vase usually rhymes with "face," which was its original English pronunciation, though modern British speakers say it so it rhymes with "blahs" instead.