I'm gonna take a shot at this...although I agree with all the above (except that batteries are rated in mill-Amp-hours, which work out to units of charge, not energy), I think there might be easier ways to explain it to a layman. There's only really three or four main concepts you have to understand, but each concept has several little details. Don't worry. All the little details relate in ways that are easy to understand, so long as you don't let yourself be intimidated and give yourself enough time to soak it all in.
First concept: When we use electricity, all we're doing is giving a bunch of electrons a push (voltage) so they move through an obstacle (resistance).
The most basic unit of electricity is an electron, or charge. We call a bunch of charges a "coulomb", but don't worry about that. Batteries are rated by (among other things) the number of charges they can hold. They say "mAh" which stands for "milli-Amp-hours", but that's just to confuse you. If a battery is a bucket, then we'd measure the bucket in gallons or liters instead of mAh.
The push we give each of those charges when we use electricity is called "voltage", which we rate in terms of joules of energy given to each coulomb of charge...but that's just to confuse you. It's easier to say "volts". If your e-cig was a garden hose, the voltage would be the water pressure.
The push we use (the voltage) gives each electron energy, the obstacle wears them down. The reason we do this, is that the obstacle turns the energy it takes from each electron into something we can use. In your cartomizer, the coil is turning electrical energy stored in your battery into heat, which is useful for vaporizing.
There's also a rating for the number of electrons we can push through a given obstacle in a given amount of time. We call it current, and we rate the current in terms of coulombs ("bunches") of charges per second...but that's just confusing. It's easier to say "Amps". In the example of the garden hose, it'd be "gallons per minute".
There's gotta be a rating for the size of the obstacle we're pushing all those electrons through, right? The obstacles (resistances) are rated in Ohms. The more ohms, the bigger the obstacle.
Next big concept: You can have one obstacle in a circuit, or you can have several. One of the basic rules of electricity is that the obstacles (in this example, your cartomizer coil) will always take away all the energy you give the electrons, no more and no less. The electrons will always start off full of energy, and end up empty after they get through all the obstacles.
If you put a bunch of obstacles (resistances) one after the other in a row, then the amount of energy each obstacle takes from a given electron will be some portion of the total push you gave them to start with. Put 3 equal obstacles in a row, for example, and each will take 1/3 of the energy present in each electron...it just works out that way. Also, the resistances add up. Put 3 3-ohm resistances in a row, and you get 9 total ohms. Whenever you have multiple obstacles in a row, and you force each electron to go over each of them one after another, it's called a "Series Circuit".
On the other hand, if you put 3 equal obstacles next to each other, and give each electron their choice of which obstacle to go over, then each obstacle will rob the full push, or voltage, from each electron that goes over it. When resistances are laid out side-by-side, and each electron has its choice of which to use to get to the other side, we call this a "parallel circuit". Without getting into the math behind it, just know that when you put these obstacles in parallel, they don't add up...in fact, when you look at them as a system, and equate the three in terms of a single obstacle with a resistance, that obstacle would be smaller. It's kind of like when they open up extra toll booths on the interstate. Yeah, you still gotta slow down to go through, but you don't wait as long, and more cars can get through in the same amount of time. Same thing happens to electrons when you open up a circuit with a bunch of parallel paths for them to take...more get through. You know those "dual coil" cartomizers? Those coils are in parallel. More on that later.
Next big concept: The amount of current is always a balance between how much push (voltage) you're giving your electrons, and the size of the obstacle they go over (the resistance). The relationship was defined a long time ago by a really smart guy, and it goes like this: The amount of voltage equals the current times the resistance. The equation we write is V = I*R Not so hard, right? But it's saying a lot. It's saying that if I hold the voltage steady, like your e-cig tends to do, then lower the resistance (like, say, switching from a regular coil to an "LR", or low-resistance coil), the amount of current goes up. If each charge in that current has an equal amount of energy (a steady voltage), and the current goes up, then there must be more total energy being handed out and harvested as heat by the resistance....and if there's more energy, that means more heat, and that means more vape!
So, if you've got a 3.7 Volt battery, and you use an LR (low resistance) coil, then you get more vape than you would with a high resistance coil. If you're smart, though, you'll remember that there's only so many drops in our bucket, so to speak...higher current means more electrons are flowing, and that means that our battery is running out of electrons faster. If, on the other hand, we raise the voltage and leave the resistance alone, we get more vape as well. Or, we could combine the two: Raise the voltage and lower the resistance. Even more vape...but there are limits.
Power is another great concept that comes into play...it's basically a measure of how fast we're using up energy. In the example above, we're using a low resistance coil so that more current flows, and we use energy faster. Using energy faster = more power. More power = more vapor. There are limits, though, and we hope we don't run into them. If you're thinking, "I'm gonna put a bunch of low-resistance coils in parallel like that example earlier, and get a super-low total resistance, then I'll get super-high current, and I'll get super-big clouds!", then you're going to run into those limits really quick. See, a battery can only put out so many volted-up electrons at a time...their storage and release of electrons is a chemical process...just because it obeys our nice V=IR equation for some resistances and some voltages, doesn't mean we can push those resistances really low and those voltages really high and get away with it. The relationship between Voltage, current, and resistance only works when the materials you use hold up to the punishment you give them. The battery will sometimes let the voltage sag in such a situation (each electron will get less push because it can't keep up) or, in extreme cases, the battery can fail altogether. Another limit to the power we can use is the coil itself...too much power means too much heat is produced, and it's possible to melt your coil.
Anyway, I use a 3.7 volt system with an 1100 mAh battery, and I get good results with a 1.7-ohm single coil carto.
when it comes to all this jargon, electrical stuff has always scared the crap out of me in a big way
