The atomiser, the upper part of your electronic cigarette, has various designations depending on the system it uses, and allows you to achieve different feels.
Clearomisers
Clearomisers are devices that vapourise e-liquid. They contain a tank and a ready-made coil, made from fibre (silica, cotton, etc).
There are clearomisers with top-coils as well (like the Kanger T2), which produce a warm vapour in your mouth, or bottom-coil devices with a more tepid/cold rendition, such as Geek Vape's Zeus Sub-Ohm tank.
Rebuildable atomisers
Rebuildable atomisers work like clearomisers, since they vapourise e-liquid as well, but it's up to the user to 'build' the coil, using some resistive wire (kanthal, SS316, Nichrome, Ni200, etc) and fibre (cotton).
Thus, experienced vapers can enjoy the flavour rendition and performance of their atomiser by making their own custom coil to suit their needs and vape at the power that offers them the best feel.
Drippers
Drippers are rebuildable atomisers that do not have a tank. The concept is the same, since you need to make your own coil(s). The advantage of this equipment is that it offers even purer flavours than with a classic atomiser, and you need to pour drops of e-liquid onto the coils to soak them after every few puffs.
Thus, the dripper allows you to change flavours at will and even taste e-liquids to try out new flavours. Furthermore, it is a very useful tool for those who make their own e-liquid (DIY) so they can perfect their recipes.