Quantization is the combination of dividing (by the quantizer) and rounding a real quantity into a small discrete number. A quantized value is more compact to store. however, quantization introduces error, because after multiplication the new and old values may differ.
When carefully used, one can make sure that the amount of error introduced by the quantization does not become audible. As a result, this is an important part of all lossy audio compressors.
Quantization can be combined with a transform that reduces the amount of quantization error for the typical case.