Warning: Wikipedia contains spoilers
There are two ways this trick is commonly performed. Both methods involve misdirection of the audience to suggest the rope is cut in two when it is in fact not. This is usually accomplished by looping the rope in the palm of the hand while showing two additional rope ends to give the illusion the magician is holding 2 separate pieces of rope.
The additional ends either come from one end of the rope which was cut as though it was the middle, or by palming a trick piece of rope of the same type.