All flowers, including tube flowers, can have up to four parts: sepals (collectively called the calyx), petals (collectively the perianth), stamens and pistils. In tube flowers, the perianth, perhaps along with the calyx, is joined at the bottom, creating the tubal shape of the flowers. Tube flowers are called gamopetalous flowers.
If a plant possesses sepals, they will be on the bottom of the flower, closest to the stem. They may look like a cup or a pedestal, holding the rest of the flower. On a gamopetalous flower, find them at the bottom of the floral tube.
The job of sepals is to protect the flower while it is in the bud stage. Closed over the rest of the flower, sepals are most often leaf-like, coming in colors like brown or green. Sometimes, though, they look like petals and can be nearly indistinguishable from them. Indeed, sepals and petals are related enough to be referred to together as the corolla of a flower. They are also both considered to be accessory parts of a plant, because without them a plant can still reproduce. Of course, gamopetalous flowers will always have petals, at least, to form the tube that distinguishes gamopetalous flowers.
Petals are the most recognizable part of a flower and, on a gamopetalous flower, create shapes like tubes, funnels or the bells of trumpets.
The reason petals are showy is to attract pollinators, usually bugs, who will either pick up pollen or deliver it so fertilization can take place. The end game is reproduction; fertilization results in seeds and fruits. The tube shape of some gamopetalous flowers have specifically evolved so that only certain types of pollinators can reach the nectar and pollen. Butterflies and hummingbirds are among the specially invited pollinators of many tube flowers. Long tongues and beaks can plumb the tube of the flower to get at the nectar---and the pollen---inside.
The androecium is the collective term for the stamens of a flower. Stamens are male parts, so only male or androgynous flowers possess them.
Stamens are each composed of a filament topped by an anther. This anther, which is often lobed, produces pollen. Within pollen are sperms. For a flower to be fertilized, the pollen must make it to female parts of flower, this accomplished by pollinators.
The female parts of a flower are collectively called the gynoecium. These parts are called carpels, which are often fused together into a single structure called a pistil. At the top of each carpel is a stigma, where pollen lands. Holding up the stigma is a stem-like tube called a style, through which sperm travels down to an ovary located at the base of the carpel. Within the ovary are eggs---ovules---awaiting fertilization.
Of course not all gamopetalous flowers will have carpels. Carpels are found only in female or androgynous flowers.