A flower garden is a form of garden usually grown for decorative purposes, centering primarily on the kinds of flowers produced by the plants involved. Because flowers bloom at varying times of the year, and some plants are annual, dying each winter, the design of flower gardens can be sophisticated, taking such matters into consideration to keep blooms, even of specific color combinations, consistent or present through varying seasons.
These have grown in complexity over the years, and are sometimes tied in function to other kinds of gardens, like knot gardens or herb gardens, many herbs also having decorative function, and some decorative flowers being edible.
One simpler solution to flower garden design, growing in popularity, is the pre-planned "wildflower" seed mix. Assortments of seeds are created which will create a bed that contains flowers of various blooming seasons, so that some portion of them should always be in bloom. The best mixtures even include combinations of perennial and biennials, which may not bloom until the following year, and also annuals that are "self-seeding", so they will return, creating a permanent flowerbed.
Another, even more recent trend is the "flower garden in a box", where the entire design of a flower garden is pre-packaged, with separate packets of each kind of flower, and a careful layout to be followed to create the proposed pattern of color in the garden-to-be.
Many, if not most, plants considered decorative flowers originated as weeds, which if attractive enough would sometimes be tolerated by farmers because of their appeal. This led to an artificial selection process, producing ever-prettier (to humans) flowers. This is thought to have occurred for the entire history of agriculture, perhaps even slightly earlier, when people tended to favored, naturally-occurring food-gathering spots. This may also explain why many flowers function as companion plants to more useful agricultural plants; they had evolved that symbiotic relationship with the food plants before either was domesticated, and therefore was found in the same area, convenient to be selected as an attractive plant.
Once domesticated, though, most flowers were grown either separately or as part of gardens having some other primary function. In the West, the idea of gardens dedicated to flowers did not become common until the 19th century, though in fact many modern gardens are indeed flower gardens.
Flower gardens are, indeed, a key factor in modern landscape design and even architecture, especially for large businesses, some of which pay to have large flower gardens torn out and replaced entirely each season, in order to keep the color patterns consistent.