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Monotonicity means that the output binary code always increases as the input voltage increases. In a non-monotonic A/D, there will be one or more points in the output code where the output code indicates that the input has decreased, when in fact it has increased.
Another way to look at it: If you put in a linear ramp, and connect the output to a perfect D/A, the output will be a staircase which looks like the input but with quantization (LSB) steps in it. If the A/D is non-monotonic, there will be one or more places in the output waveform where the slope reverses.