What is a Gaussian kernel?

I am trying to understand a paper where the term "Gaussian Kernel" is used often. Upon first reading it I thought kernel and $$\sigma$$ (standard deviation) were synonyms, but upon reading this document, it sounds like the sigma is one of the parameters of the kernel, but it isn't one to one with it.

What exactly is the Gaussian kernel if not the $$\sigma$$ of the distribution?

• You can try to watch this.. – Peanojr Feb 26 at 16:42