Plants have the marvellous property of being able to propagate not only by seed but also from just a piece of plant tissue.
This natural phenomenon, used to propagate many ornamental plants, is called vegetative propagation.
Vegetative propagation is faster than obtaining new plants from seed. It also lets you propagate plants that produce few if any seeds, to “rejuvenate” some plants and, most importantly, to preserve a given plant’s characteristics.
There are various methods of vegetative propagation and any plant may be propagated by using at least one of these methods. Some of the techniques used for indoor plants are explained in detail here.