Taking cuttings and striking them is a way of growing a new plant from a piece cut off from another plant.
The most successful way of taking cuttings varies widely depending on the type of plant. Some cuttings need to be of soft new growth, some hard, some taken in winter while the plant has no leaves, some in spring when it is vigorously growing, still other plants can be grown from only a piece of root or a leaf. Some need to be let dry a little first (hardened), some need special hormones, but as a general rule all cuttings need to be kept slightly moist so they do not die before they have their own root system.
The cuttings in the photo have been left to stand in water and have grown roots.