Tulips originated in the Far East in present-day Kazakhstan and surrounding countries. In the sixteenth century, this area was conquered by Süleiman the First, and became heavily influenced by the Ottoman Empire. The Tulip, recognized as a special and unique flower, was taken along to Turkey where it was introduced to the gardens of the richest dignitaries.
The Tulip became extremely popular, and a symbol of power and wealth - the Ottoman sultans even began to wear Tulips on their turbans.
The modern name for Tulip is the latinized version of the Turkish word for turban, "Tülbend" which ultimately derives from the Persian "Dulband", meaning round. It was likely chosen because the shape of the flower was thought to resemble a turban.
A supplemental fun fact - the Turks themselves refer to the Tulip as "Laleh", the name that arrived with the flower from Persia. In Arabic script it literally meant 'Flower of God', as "Laleh" is written using exactly the same letters as Allah.