A cultivar is basically a variety within a species
Cultivars can have a number of different origins. Plants found in the wild may develop a different form when propagated in the garden; if this form is retained through propagation then it may be called a cultivar.
A cultivar may be found in a batch of seedlings, or a chance seedling growing in the garden. Cultivars may also be developed via hybridization; where deliberate crosses are made between different species the hybrid is known as a cultivar.
Cultivars do not grow naturally in the wild, and are generally propagated by layering, cuttings, division, or other means. If they are propagated from seed the cultivar will not breed true. All hybrids are cultivars, (in that they will not breed true from seed) but not all cultivars are hybrids.
There are many reasons for growing or using cultivars; when using a cultivar for ornamental reasons, the many additional (and often quite beautiful) forms are the main reason to plant a cultivar. When used in this way a cultivar is sometimes (often) less hardy and resistant to disease and pests than the root species.
Strangely cultivars can be used to increase the hardiness and resistance of a species. To do this more than one cultivar is grown at the same time. Examples of this are found in the use of cultivars in turf grass species.
When a lawn is planted with only a single species of grass, that species should include different cultivars. Turfgrass cultivars with resistance to different diseases and environmental conditions should be mixed. When the stresses on the lawn change those cultivars with resistance to that stress survive, and thus the lawn survives.
It is the greater genetic diversity provided by the differing cultivars, that improves the disease, insect resistance, and the general adaptation of the turf under differing environmental conditions.