Though flowers can seem wildly different from each other--some sweet and understated, others as flashy and dramatic as a tango--they are actually quite similar. All flowers are capable of producing only a limited number of parts. Since flowers are the reproductive organs of plants called angiosperms, the parts include male and/or female parts located on the inside center of the flower and accessory parts that occur only to protect the all-important reproductive sexual parts. Complete flowers have four parts; incomplete flowers have fewer.
The calyx of a flower is the "accessory" part of a flower since it is not directly involved in reproduction, though it may play a role. Petals and sepals together make up the calyx. Both serve to protect the innermost parts of the flower.
Sepals are located on the outermost section of the flower. They are leaf-like structures that you are likely to easily recall when imagining a rose.
Petals occur just inside the sepals. If they aren't very showy, the flower is likely wind-pollinated. If they are colorful, large and scented, with nectar at their bases, the petals are trying to attract creatures to help with pollination.
The male parts of a plant are collectively called the androecium and are composed of stamens and anthers. Stamens occur in a ring just inside the petals. Each is composed of a filament topped by an anther, which is usually lobed. This anther produces pollen. Within the pollen are sperm. If all goes well, wind or a creature will pick up the pollen and deliver it to the female parts of flowers.
Female parts of a flower together go by the term gynoecium. A flower's gynoecium is composed of at least one carpel, often fused together to form a pistil. The gynoecium is located at the very center of any flower, provided the flower is either female or a hermaphrodite. A flower without the gynoecium, then, is a male flower.
A carpel or pistil has three sections to it. The base--the ovary--is bulbous and contains one or more eggs. Rising up from the base is a column called a style. Topping the style is the stigma, there to receive pollen carried in by creatures or blown in by wind. Once the pollen is caught, the sperm moves down the style to unite with egg. This fusion ultimately becomes a seed.