The inverse operation of convolution
. If f(x) = g(x)*h(x) (the convolution of functions g(x) and h(x)), deconvolution is the process of recovering g(x) when you only know f(x) and h(x).
An example of convolution is the blurring of images. There g(x) is the original image, h(x) is the "blurring function" and f(x) is the end result. For example, a defocused lens has a characteristic h(x) (aka point spread function). Deconvolution can be used to restore the original image g(x), if the resulting f(x) and the blurring function h(x) are known.
AFAIK, deconvolution has no simple physical counterpart and it must be done computationally. To do that, it is common to work in a matrix or fourier representation. That way, convolution is basically multiplication, and deconvolution is division. Of course you have to transform back into real space to use the result.
Mathematically, it should be noted that convolution and deconvolution are linear operations. Therefore they do not lose any information. This is the basis for the surprising fact that blurred signals can be recovered. Unfortunately there is also blurring due to other effects such as noise, and these cannot be restored perfectly.