I am answering because I believe none of the other posts address the question completely and with the audience in mind.

In statistics and computer science, "kernel" indeed has many different meanings. In your case, you can replace "every step is given by a Gaussian kernel" with "every step is given by a random draw from a Normal/Gaussian distribution." (There should probably be an accept/reject step next, which you did not mention.) Metropolis-Hastings is used for search or integration, and either way it must explore the space of possible parameter values. For the math to work, they are usually randomized, and the Normal/Gaussian family is useful for that because it is simple and well-studied.

Some of the other meanings of "kernel":

Kernels appear in the context of kernel density estimation, which is a smoother alternative to histogramming. This is similar to the meaning in Ethan's answer--it's a probability distribution.

They also appear, as Matted mentioned, in machine learning, where the kernel function generalizes "parallel-ness" for two vectors in an abstract space. By "generalizes", I mean it adds options while preserving essential properties. Some algorithms can be painlessly adapted by replacing regular parallel-ness, measured by vector dot products, with kernel evaluations.

Matted also mentions differential equations and random diffusion processes. For phenomena that evolve over time, these "kernels" give a complete mathematical account of the inner workings. This is similar to what happens in metropolis-hastings, which is like an artificially constructed diffusion process.

In mathematics they can refer to a "dead zone": the kernel of a function (or matrix) includes everything that gets sent straight to zero by that function (or, when you multiply by the matrix).

In computer science, I don't know what a kernel is, but there is (at least) another meaning, as in the IPython Notebook's warning "Your Python kernel has died."

Kernels also refer to the seeds of corn. :)

I think the only thing trivial about your question is it is not directly related to bioinformatics, rather it is a statistics question.