Discrete convolution in digital signal processing is used (among other things) to smooth sampled signals using a weighted moving average. It also has many applications outside of signal processing.
IDL has two functions for doing discrete convolution: BLK_CON and CONVOL. BLK_CON takes advantage of the fact that the convolution of two signals is the Inverse Fourier transform of the product of the Fourier transforms of the two signals. BLK_CON is faster than CONVOL, but not as flexible. Among the many applications for discrete convolution is the implementation of digital filters. See the example in the Finite Impulse Response (FIR) Filters.