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It means that the amplifier has a non-linear relationship between the input signal and the output signal.
For example the gain at a lower signal voltage might be slightly different at a higher voltage.
Say the input was a sawtooth with straight edge ramp, the output would then be a sawtooth with a curved ramp.
That's nonlinear distortion.
Non-linearity depends on symmetry of AC signal. If a symmetrical signal goes IN you expect it to be the same going out. Normally beta reduces when Vce tends to get near 2V and lower then compressing the peak and causing harmonic and other distortion.
In RF the test is called 3rd order intercept, which you may look up if interested.
In Audio they use total harmonic distortion or %THD.