Ropes are created at the clothier's shop with one cloth, using the clothier skill.
Ropes are not actually a distinct item type - they are merely what chains are called when they are made of cloth. They are both listed under the 'chains' heading in the z-stocks menu, are stored in finished goods stockpiles, and are generally interchangeable.
They are used to make traction benches, build wells, restraints and minecart rollers.
Taking a rope with you at embark lets you construct a well more quickly. While usually it's much cheaper to take raw materials and produce ready goods after embark, item value of a rope is 20 vs. 12 of the thread. The dwarves will not enjoy using a base quality item as much, but cost-wise it matters 3 times less than the mechanism.