There is a tradeoff between image quality and degree of quantization. A large quantization step size can produce unacceptably large image distortion. This effect is similar to quantizing Fourier series coefficients too coarsely; large distortion would result. Unfortunately, finer quantization leads to lower compression ratios. The question is how to quantize the DCT coefficients most efficiently. Because of human eyesight's natural high frequency roll-off, these frequencies play a less important role than low frequencies. This lets JPEG use a much higher step size for the high frequency coefficients, with little noticeable image deterioration.
The quantization matrix is the 8 by 8 matrix of step sizes (sometimes called quantums) - one element for each DCT coefficient. It is usually symmetric. Step sizes will be small in the upper left (low frequencies), and large in the upper right (high frequencies); a step size of 1 is the most precise. The quantizer divides the DCT coefficient by its corresponding quantum, then rounds to the nearest integer. Large quantums drive small coefficients down to zero. The result: many high frequency coefficients become zero, and therefore easier to code. The low frequency coefficients undergo only minor adjustment. The page explains how many zeros among the high frequency coefficients leads to efficient compression.