The difference between the actual analog value and quantized digital value due is called quantization error. This error is due either to rounding or truncation and can sometimes introduce noise to signals.

Quantization noise is a model of quantization error introduced by quantization in the analog-to-digital conversion (ADC) process in telecommunication systems and signal processing. It is a rounding error between the analogue input voltage to the ADC and the output digitized value. The noise is non-linear and signal-dependent

Please click on the wikipedia link to hear a sample of how bad this noise can get.

Source:

http://en.wikipedia.org/wiki/Quantization_error