Convolution can be explained in just a few words: it is a local weighted average (the weights can be negative). This of course does not explain how to use it or what its properties are. For this we refer to the following sources:
Ian T. Young, Jan J. Gerbrands and Lucas J. van Vliet, Fundamentals of Image Processing.
Alan V. Oppenheim, Alan S. Willsky and I.T. Young, "Signals and Systems", Prentice-Hall, 1983.
Anil K. Jain, "Fundamentals of Digital Image Processing", Prentice-Hall, 1989.
"The Digital Signal Processing Handbook", Vijay K. Madisetti and Douglas B. Williams (eds), CRC Press + IEEE Press, 1998.
Kenneth R. Castleman, "Digital Image Processing", Prentice-Hall, 1996.