First of all, not all flowering plants always bear flowers. Also, plants usually flower only during their flowering seasons, which sometimes is only a very brief period. Therefore, even on certain flowering plants you may seldom or never see a flower.
Flowers are the sexual organs of a flowering plant. The picture above tells the story, though at first glance the story may not be obvious.
The picture shows an item about an inch (2.5 cm) long which I just snipped from the cucumber vine in my garden. The yellow part in the picture's right side is a shriveling cucumber flower. It is drying up and shriveling because it has finished its "job." The flower's "job" has been to attract an insect pollinator to itself.
And that's what happened. The insect pollinator brought pollen grains from the male parts of another cucumber flower and left them on the female parts of the flower above. Thus the flower in the picture has already been pollinated and the bright part, the corolla, is about to fall off because it's no longer needed. In a sense, the green thing at the left in the photo is a fast-growing-up "baby" cucumber.
Flowers are the means by which flowering plants have sex. They are composed of male and/or female parts. Flowers may have other structures as well, to help the sex get accomplished -- such as colorful petals to attract pollinating insects.
Keep in mind that when a flowering plant has something bright and pretty on it, that bright and pretty thing isn't necessarily a flower. The White Clover, Trifolium repens, shown at the right is one of the most common plants in typical backyards, and that whitish, roundish thing at the plant's top is not the flower. It's a cluster of about 40 flowers. The orange-framed inset shows about 1½ flowers.
Therefore, when you meet a plant that's flowering, the first thing you might do is to confirm for yourself that you're seeing a flower, and not a cluster of flowers, or something else entirely. You need to know you're seeing a flower when you see one!
On our Standard Blossom page you find out how to do this by learning about a typical flower's main parts. On our Blossom Arrangement page you can see various ways flowers arrange themselves on plants.