I understand that Ohms are resistance and the higher the number the more resistance, but my question is what exactly does more resistance serve???
I'll use an automobile analogy.
The max torque that your engine can deliver varies with RPM. Similarly, the max voltage that an amplifier can deliver varies with the current.
Power from an engine is torque times RPM. Power from an amplifier is voltage times current. An engine's (or amplifier's) powerband has a sweet spot where the power is the highest.
To get the most power to a car's wheels, you want to present a load to the engine that has it operating in the sweet spot of its power band. In a car, this is done with gearing.
A transformer is the electrical analogue to gearing. Vacuum tube amplifiers usually have a transformer between their output and the speakers, sometimes with multiple taps--analogous to a car having a transmission with a choice of gears. Solid state amplifiers usually have no output transformer; to enjoy the sweet spot of the amplifier's powerband, you need to connect a load with a compatible impedance. ("Impedance" is the term of choice rather than "resistance" when dealing with AC signals; both are measured in ohms.)
An engine and an amplifier are different beasts, in that a dyno plot and an analogous voltage/current plot for an amplifier will show
differently shaped kinds of curves--but both of them are curves rather than simple straight lines. The max power available when you connect an 8 ohm speaker to an amplifier optimized for 4 ohms depends on the specifics of the amplifier's power curve; saying it's one-half what you'd get with a 4 ohm speaker is only an estimation.
That's the main idea. It's more complicated in that the impedance of a speaker varies with frequency; a speaker's "8 ohm" or "4 ohm" rating is a nominal value meant as a rough guide for selecting a compatible amplifier.