OK- now we got the basic part- a greater load is less resistance, less of a load is higher.
There is more of a take-away than this however. It has to do with power vs distortion (and also in the case of tubes bandwidth may be affected).
**If** high fidelity is your goal, your amplifier dollar investment will be better served by a loudspeaker of higher impedance (all other things being equal). This is because, regardless of the amplifier technology (tube, traditional solid state or class D), the distortion will be higher driving lower impedances. This is both measurable and audible.
**If** your goal is sound pressure, there is a slight argument for a lower impedance speaker (in the case of an 8 ohm speaker, a 3 db higher sound pressure will be had if you go to 4 ohms) all other things being equal. This however is only true if you have solid state, and still might not be true unless the amplifier can support the additional current required to double its power (a 3db increase in volume requires a doubling of power, and cutting the load impedance in half could win you that 3 db).
The kind of distortion that is increased in all cases by the use of a lower impedance load is audible, despite the increase usually being rather slight. This is because the additional distortion produced is of the kind to which the ear is extremely sensitive: higher ordered harmonics and additional IM distortion.
The presence of distortion obscures low level detail due to the ear’s masking principle. The ear/brain system converts all forms of distortion into tonality; thus the slight additional distortion contributes to brightness and harshness.
As a result, generally speaking, any amplifier will therefore be smoother and more detailed driving a higher impedance load. Its a simple fact that you can make an amplifier work hard by making it drive a difficult load, but that it not the same as having it sound its best!
I know that many people have fallen in love with certain low impedance speakers (many of which have excellent properties) and they are also quite happy with the combination of amp and speaker that they have. All I am pointing out is that if that same speaker were somehow 8 (or better yet 16 ohms) instead of 4 ohms, it would sound smoother and more detailed with no real downside except a slight amount of power in the case of solid state amps (tube amps would make the same or slightly higher power, likely with wider bandwidth as the output transformer is more efficient driving higher impedances).
For speaker designers, a simple way to make their speaker seem smoother and more detailed is to simply make it higher impedance...