The ten-penny answer is that it's a plant which during some part of its reproductive cycle produces flowers, and the female portion of these flowers must consist of at least a pistil, inside which reside ovules developing into seeds. If these terms and concepts throw you for a loop, you might want to visit our link dealing with basic flower structure before continuing.
Our ten-penny definition needs to include the part about pistils and ovules because some plants, such as pine trees and other conifers, produce flower-like reproductive structures which, technically, aren't true flowers.
Ferns, mosses, lichens, and fungi have nothing even looking like flowers. Neither do one-celled microorganisms.
The Drummond's Aster, Aster drummondii, at the right, just plucked from next to my door and scanned, is clearly a flowering plant. However, I'll bet that right now I could go into your backyard and find some items that you couldn't say for sure whether they are flowers or not. In fact, even the aster flowers in the picture are more curious than they seem. On our Composite Flowers Page you can see that the things in the picture you probably think are flowers are actually clusters of flowers.
If your backyard is a typical one with lots of grass, some bushes and trees that lose their leaves when winter comes, maybe some garden flowers or vegetable plants, and possibly a few weeds, then all or nearly all of the plants you see when you look around will be flowering plants. The most conspicuous backyard plants that are not flowering plants include pine, spruce, and other conifer trees, and yew bushes.
Therefore, plants in most backyards confirm the fact that flowering plants are the most conspicuous, most diverse, and most economically important group of plants on earth today. If flowering plants were to suddenly disappear, life on Earth as we know it would come to a screeching halt. The world's big rain forests, so important for producing oxygen for us to breathe, would vanish; soil erosion from denuded slopes would choke our rivers with silt; the landscape would become barren and sterile.... Nearly all our food comes from flowering plants, or animals that eat flowering plants.
These are scary thoughts when you reflect that a large percentage of flowering plants require animals, particularly insects, to pollinate them, and these animals are very sensitive to insecticides and other toxic chemicals mankind unceasingly pumps into the environment.
Flowering plants, in terms of the history of life on earth, are fairly "new inventions." Life on earth is reckoned as having dawned a little over four billion years ago. Microscopic blue-green algae appeared in the oceans around 3.5 billion years ago. Other forms of algae, as well as ferns, fungi, mosses and other non-flowering plants gradually evolved and ultimately, during the Silurian Period between 443 and 417 million years ago, plants arose with adaptations enabling them to live on dry land. Many millions of years passed, and then only about 375 million years ago did the first forests appear.
And even then, there were no flowering plants. The first forests consisted of ferns and fern-like plants. Conifer trees, non-flowering ancestors of pines and spruces, developed approximately 285 million years ago. Finally, it was only long after the first mammals and the first birds began gracing the landscape that the first flowering plants came into existence -- only about 135 million years ago. Even then it wasn't until 80-90 million years ago that flowering plants began dominating the landscape.
But these flowering plants turned out to be worth waiting for! The new flower/fruit/seed manner of reproducing was much more flexible and effective than the old ways. Evolution sped up, and new-fangled flowering plants suddenly began occupying niches that hitherto had remained vacant. Sometimes a dozen seeds produced by these new species of flowering plants produced more offspring than a million fern or fungus spores falling onto the same ground!
Consequently, no matter what corner of nature study we ultimately gravitate to, it's hard to progress far without a basic understanding of what flowering plants are all about, and that's why we give such attention to them at this site.