Smoothing Kernel
The kernel for smoothing, defines the shape of the function that is used to take the average of the neighbouring points. Kernels are often synonymous with convolutional-filters.
Gaussian Kernel
A [see page 15, kernel] with the shape of the Gaussian distribution.
For example:
1 1 2 1
---- 2 4 2
16 1 2 1
Remember a filter must sum to 1, that's why we divide by 16.