What is Quantization error?

The error that arises when rounding a continuous analog value to a digital value with a finite number of bits. At most half of one LSB.

Quantization error in the explanations

More bits mean a smaller LSB and smaller quantization error.
What is the maximum quantization error of an ideal AD conve…
Quantization rounds each sampled value to one of a finite set of levels, and the difference from the original is the quantization error—at most ±1/2 LSB in an ideal ADC and smaller with more bits.
What is the error caused by quantization in AD conversion c…
For small or slowly varying inputs, quantization error correlates with the signal and appears as harmonic distortion.
What is the main purpose of deliberately adding a small noi…