What does the convolution mean, what is the convolution philosophy
I'm somewhat in the same situation as you @Jony. But I'm working currently on a project involving audio processing, and I had to read a lot about convolution and related topics in the last few days.

I'm not sure I gained an intuitive understanding of convolution--esp. convolution vs. correlation-- but, to quote another answer, "Convolution in the time domain is equivalent to multiplication in the frequency domain." So it becomes obvious it may have a usage in filtering applications.

Wikipedia hs also a couple of nice animation that shows you how the convolution of two functions is related to the area of their intersection:




Depending on your field of interest, this may give you some applications idea. As the last word, let me repeat I'm very new to this topic, so take this answer with a grain of salt--and I would gratefully stand to be corrected by more experienced users