Impedance: basically the resistance of a speaker. Your amp can overheat or fry if it's too low. If it high, and you want to crank it very loud, you may send your amp into clipping....which hurts your speakers (to a certain extent; but that's for another thread

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Frequency response; the range that a speaker can reproduce.
Usually like: 60-16,500hz, +/-3.0db.
That means from 60-16,500hz, there's a + or - 3db variance between the peaks and valleys of the speakers output.
Note that even speakers with 12inch woofers usually start rolling off (AKA the bass response starts diminishing) around 30hz.
My own 15inch Dayton DVC home theatre sub starts rolling off @ 40hz, BUT because the (sealed) box is SO big , it rolls off VERY smoothly.....something like 8db/octave instead of the typical 12db/octave rolloff of sealed box.
That's why I can push 115db @ 20hz in room
Sorry if I confused you
Pwer Handling; how many watts the driver can thermally handle.
Like say you have a 10inch subwoofer that's rated for 600watts RMS. It may be able to handle that all day long, but if you were to run music through it @ 600watts RMS, it would likely bottom out (AKA; the cone would move too far and hit the magnet or rip the foam surround, etc etc).