A long piece of thin rope is shown to the audience. The magician bends the rope in half and uses a big pair of scissors to cut it into two pieces. The two pieces of rope are clearly shown, but when the magician holds their ends together and makes a magical gesture, they become a single piece of rope again.
Although the "rope" is indeed rope on the outside, on the inside it's a yard-long piece of licorice (the use of this gimmick is so old that the term "licorice rope" has even become part of American venacular).
This rope-covered licorice can be cut at any point with a sharp pair of scissors. To rejoin the halves, the magician simply squeezes the two bare ends together, causing the still-sticky freshly cut licorice ends to adhere to each other, creating the illusion of a restored rope.
After the performance, the magician may eat the prop's filling as a tasty snack.