What does "kernel based" mean?
In general, a kernel is a function that acts as a parameter to some algorithm.

Filtering: For example, it's possible to call the impulse response of a filter $h[n]$ a kernel, so that it is the parameter that defines the filter operation:
$$
y[n] = h[n] * x[n].
$$

The use of the term kernel in the filtering context is much more common in 2D filtering or image processing.  The link talks about the kernel being a matrix, but really it's just a sampling of the function that is the "true" kernel.

PDF Estimation: Kernel-based methods are often used in other contexts, too.  For example, when estimating the probability density function of a random variable, kernel-based estimators are often preferable to simple histogramming.  In that context, there are many different possible kernels.



Machine Learning: Finally, another context for kernel based algorithms is in machine learning.  Here, we are interested in classification of an input into one of (possibly) many classes.  Again, the kernel is a function $k(\mathbf{x}_i,\mathbf{x}')$ that parametrizes the algorithm and there are many possible selections.