Cartomiser
(US: Cartomizer)
What is it?
The cartomiser (cartomizer) combines the atomiser of an electronic cigarette with the refill.
An example of a cartomiser is the NJOY DUO.
Disposable
Sometimes cartomisers are used to refer to disposable electronic cigarette, designed to be used once and thrown away. Our own are permanent - the cartridge/atomiser is disposed of but the batter is kept.
Background
Early versions of electronic cigarettes came in three parts: 
a battery, an atomiser, which was screwed on to the electronic cigarette, and a cartridge, which was pushed on to the atomiser.
Unfortunately, the atomiser was the part most likely to fail. If the atomiser did fail, the user would be without the use of his electronic cigarette until the part had been replaced.
Atomisers also increase the difficulty of changing the catridge and the cleaning, which should take place weekly.
A lot of dedicated vapers don't mind the maintenance that comes with old style electronic cigarettes - in fact, it can be part of their passion. But for newcomers and for those who just want a quick alternative to smoking the maintenance can be off-putting.
Advantages
The cartomiser means that if you have on atomiser that fails you can still continue to smoke - the most you can lose is a cartridge. There is no cleaning, and changing the cartridge becomes a simple and easy process.