One of the ways I was taught electronics back the day was to think of the wire as a water hose. Resistance is the diameter and length of the hose, voltage is the water pressure, amperage is how much water is flowing through the hose..
Higher resistance is a skinnier or longer hose and allows less flow, lower resistance is a fatter or shorter hose which allows more flow just as with water hoses. But in this case the water is electrons, which generate heat as they flow.
Power or watts is simply volts x amps. Or pressure x flow, it is the power generated or total water the hose is producing..
So to get more power/heat (gallons out the end of the hose) you can either add higher water pressure (higher volts) or use a fatter/shorter hose (less resistance).
For any given circuit the voltage divided by resistance = amps, voltage divided by amps = resistance, resistance x amps = voltage.. it is a direct relationship between these three always. This is Ohms law.
Pretty simple really. If you have say 5 volts, and you want 8 watts of power, since power(watts) = volts x amps you just divide 8 watts by 5 volts and you get 1.6 amps of flow that you need to get to obtain that wattage.
So to get that 1.6 amps of flow you need a resistance value (size of water hose) that will restrict the flow to 1.6 amps and you find that value by simply dividing your 5 volts (pressure) by your 1.6 amps (flow) giving you 3.1 ohms of resistance needed (size of hose). Add a 3.1 ohm resistance coil to 5 volts and it will flow 1.6 amps of current and produce 8 watts of power doing so.
Sometimes it is easier to express watts as (volts x volts / resistance) when you only know your desired wattage and your coil resistance, this is just a simple substitution as we know (watts = volts x amps).
But we don't know our amperage or voltage only our resistance and desired watts.
So since ohms law says (volts / resistance = amps), we simply substitute (volts / resistance) into the wattage equation instead of amps and we then have (watts = volts x (volts /resistance)) and bobs your uncle you plug in your resistance of your coil and your desired watts and solve the equation to get the right voltage to produce your desired wattage using that resistance of coil..
As it applies to ecigs is simple, more watts = more heat, a hotter coil. Less watts = less heat, cooler coil. Too much heat and you get a burned taste, too little heat you get no vapor at all, just the right wattage gives the best flavor and vapor for a given juice in a given device for a given vapers strength of air draw.
Did that help?