Okay, you asked for it...dull electronics lesson no.1
Don't be insulted, but this is a simplification of the real world, just so that you can understand the principles involved. Many, many books have been written on the subject so I can hardly cover it all here!
I = V / R and P = V * I
Where I is current in Amps, V is Volts, R is resistance in Ohms and P is power in Watts.
Therefore, it's easy to see that if you halve the resistance, you get double the current for the same voltage, hence doubling your power output.
That's also why your 8/16 ohm speakers work...but produce half or a quarter of the power.
Okay, your next question is - why don't we just keep reducing the resistance and get even more power? Well, the components in your amp can only handle so much current before bursting into flames! eek!
The output stages of amplifiers are often designed with a particular driver resistance in mind, so it's best to stick with the manufacturers recommended resistance.
As I say, this is all a bit simplifed, but hopefully you get the idea. wink