Subtracting a wide Gaussian from a narrow Gaussian.
In edge enhance applications, a high pass filter is used. The high pass filter can also enhance the noise which also has high frequency. Difference of Gaussians remove high frequency content of noise. So it is a good method for edge sharpening, image enhancement.
The drawback is that it reduces the overall image contrast.
The practical kernel size for two gaussian (ratio) is 4:1, or 5:1.
DoG is very similar with Laplacian of Gaussian. It will get similar result when the ration is 1.6.
[update: 2/19/2013] the DoG is actually a band-pass filter, which removes high frequency components representing noise, and also some low frequency components representing the homogeneous areas in the image