Convolution means replacing each pixel with a weighted average of the nearby pixels. The weights and the area to average are determined by the convolution matrix. The unsigned numbers in the convolution file are offset by -maxval/2 to make signed numbers, and then normalized, so the actual values in the convolution file are only relative.
Here is a sample convolution file; it does a simple average of the nine immediate neighbors, resulting in a smoothed image:
P2 3 3 18 10 10 10 10 10 10 10 10 10
To see how this works, do the above-mentioned offset: 10 - 18/2 gives 1. The possible range of values is from 0 to 18, and after the offset that's -9 to 9. The normalization step makes the range -1 to 1, and the values get scaled correspondingly so they become 1/9 - exactly what you want. The equivalent matrix for 5x5 smoothing would have maxval 50 and be filled with 26.
The convolution file will usually be a graymap, so that the same convolution gets applied to each color component. However, if you want to use a pixmap and do a different convolution to different colors, you can certainly do that.
At the edges of the convolved image, where the convolution matrix would extend over the edge of the image, pnmconvol just copies the input pixels directly to the output.