@andyp13
That is indeed a good question.
Speaker design has three basic parameters:
on-axis frequency response, off-axis frequency response, and distortion.
"On-axis" means sound radiated forward.
"Off-axis" means sounds radiated in any other direction.
(1) On-axis response.
You would think that on-axis response should be completely flat.
But a speaker designed that way sounds too bright (= too much treble).
I have never heard a convincing explanation why.
(2) Off-axis response.
Radiation pattern is important because off-axis sound bounces off the
walls of the room and comes back to the listener.
Speakers radiate front, back, to the sides, and even up and down.
Unless they're sitting on the floor -- then they don't radiate down.
It's the same concept as microphone radiation patterns
(omni, cardioid, figure-8, etc). Except that it's about production
of sound instead of response to sound.
Subwoofers are usually omnidirectional.
An open-back guitar cabinet is figure-8 (also called dipole).
It's not clear what the ideal radiation pattern for a speaker actually is.
Most speakers are omni in the bass, then forward in the treble.
When a speaker has multiple drive units (woofer, midrange, tweeter),
the radiation pattern can change abruptly between them.
(3) Distortion. Ideally, a speaker shouldn't produce any. But it does.
Serious driver manufacturers do a lot of research to reduce distortion.
Harmonic distortion isn't so bad.
That's where the distortion frequencies are multiples of the original frequency.
But intermodulation distortion is bad -- it produces frequencies that aren't
present in the original music.
If you want to learn more about speakers, Floyd Toole's book is an excellent start:
Amazon product ASIN 113892136X
To give an idea what good speakers cost,
here are some low-end professional monitors ($3745 / pair):
http://barefootsound.com/footprint01/
And some high-end prosumer monitors ($2300 / pair):
https://www.dynaudio.com/professional-audio/lyd/lyd-48
