Impedance of speaker when quoted, is usually nominal impedance. However the impedance of a driver/speaker is not constant. It varies as per the frequency it is playing. It depends on the individual driver characteristics and crossover characteristics.
When a speaker spec has impedance of 4-8ohms, it means that the impedance is going to vary between 4 and 8 . It cannot be constant unless you are playing a single note sound (e.g. a particular key of a piano and nothing else). For usual music, it is a mix of various frequencies and impedance is highly variable.
If impedance of speaker is highly variable, the amplifier finds it difficult to drive. Some speakers, Like Ushers, are known to have fairly constant impedance and are easier to driver for the amp.
Change of impedance does not change the frequency the speaker is playing but definitely changes the amplitude. Speaker with lower impedance , say 4 ohm, will play louder than similar speaker of 8 ohm if volume knob is kept at the same position. This is because the amplifier pushes more current for lesser impedance at the same position of volume knob.
Lower the impedance(e.g. 2 ohm), more the current the amp has to push and puts more load on amp. Higher the impedance, safer it will be for the amplifier but the amplitude(loudness) will go down.
I hope this helps a bit.