Nature has been cloning organisms for billions of years. For example, when a strawberry plant sends out a runner (a form of modified stem), a new plant grows where the runner takes root. That new plant is a clone. Similar cloning occurs in grass, potatoes and onions.
People have been cloning plants in one way or another for thousands of years. For example, when you take a leaf cutting from a plant and grow it into a new plant (vegetative propagation), you are cloning the original plant because the new plant has the same genetic makeup as the donor plant. Vegetative propagation works because the end of the cutting forms a mass of non-specialized cells called a callus. With luck, the callus will grow, divide and form various specialized cells (roots, stems), eventually forming a new plant.
More recently, scientists have been able to clone plants by taking pieces of specialized roots, breaking them up into root cells and growing the root cells in a nutrient-rich culture. In culture, the specialized cells become unspecialized (dedifferentiated) into calluses. The calluses can then be stimulated with the appropriate plant hormones to grow into new plants that are identical to the original plant from which the root pieces were taken.
This procedure, called tissue culture propagation, has been widely used by horticulturists to grow prized orchids and other rare flowers.