Quantization takes place after the FDCT has computed and output the
coefficients. Compression is created by representing the coefficients
with no greater precision than is necessary to achieve the desired image
quality.
The 64 values are quantized by dividing each value
by a number called a quantum, and, thus, "losing" some of the
bits that represented the value. The quanta used depend upon the desired
quality and compression.
At the same time, a sort of "average value" for the block called a DC
Coefficient is computed. These DC Coefficients are related from block
to (adjacent) block, and are actually stored as the difference in the values
of the 2 adjacent blocks. These values are passed to the next step in the
algorithm, the Entropy Encoding step.
Dequantization reverses the process and introduces still more loss in the
image.