What does “kernel based” mean?

In my thesis I try to explain what kernel based methods are, especially the meaning for object detection.

I know kernel based methods like Mean- and CamShift and I know how to use them. I understand how the shift work. But: What does the kernel do, what does he describe?

I know, wikipedia have articles about kernels but I still don´t get it. :(

Q1: What could be an subset for an image?

Q2: How does the kernel project the points in an image?

Q3: Could you give me an simple example to understand kernels?

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: $$y[n] = h[n] * x[n].$$
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.