[XMPPwocky]

Fuck the frequency domain, here-

"Convolution with a kernel K" describes a system whose impulse response is K. In discrete time, suppose you have K=[1,2] and convolve [0,1,2,0] with it- you wind up with [0,1,3,2,0], if I'm awake enough for arithmetic.

Correlation with a kernel K is convolution with K time-reversed (i.e. [2,1])- you'd get [0,2,5,2,0] (again if I'm awake). Note that 5- right there, the input signal "lines up just right" with the kernel- 2x2 + 1x1. That's why it's called correlation- its output is big when the input looks like the kernel.