"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.
It's a binary operator on functions that yields a third function. It has a lot of useful properties and equivalences, like that it can be described as the product of two Fourier transforms (although that's very roundabout).
You're actually introduced to convolution in middle school when you're taught how to multiply monomials to build a polynomial (at my middle school they called it "FOIL").
> technically being simpler to compute.
They're equivalent, since the only meaningful way to "compute" a continuous convolution is symbolically, and discrete convolutions obey most of the same identities.
If one can place a lower bound on the time step resolution of a simulation then continuous convolutions are evaluated using discrete convolutions, which can represent the continuous case exactly via the Nyquist-Shannon sampling theorem.
Interestingly enough, to prove the Sampling Theorem you need to rely on the identity that multiplication in frequency is convolution in time, and to prove that it can't be realized in a physical system (breaks causality, since you multiply by a superposition of Heavisides which of course are infinitely long sinc functions in both directions of time).
And more interesting is that signals and systems is mostly applied dynamics and statistics, so it shouldn't be surprising if there's overlap.
Convolution of f and g at t is:
integration of f(x) * g(t - x)
integration of f(x) * g(t + x)
1 : a form or shape that is folded in curved or tortuous windings e.g the convolutions of the intestines
2 : one of the irregular ridges on the surface of the brain and especially of the cerebrum of higher mammals
3 : a complication or intricacy of form, design, or structure … societies in which the convolutions of power and the caprices of the powerful are ever-present dangers to survival.
After this is clear read the mathematical idea on wikipedia. After reading that, do google scholar search on the AI papers that first mentioned it. That is the way to go.