This is what is usually called a convolution. See:
http://williamson-labs.com/convolution-2d.htm[
^] for a detailed description.
The given kernel is a combination of a low pass filter and an identify kernel (with multiplier 5). That results in a high pass filter, which can be used as image sharpening filter.
By the way, the second row of your kernel should probably read (-1, 5, -1)!