Comment by rollulus

A little ELI5 for those who haven't had Laplace transforms at school, from someone who only had a Laplace 101 course, so for what's it worth: Laplace transforms allow you to convert differential equations into easier equations, and back: the differentials and integrals become multiplications and divisions. So you can take a differential equation, transform it into the Laplace domain, manipulate it, and convert it back. And that's cool because differential equations tend to appear everywhere, for instance to model springs, electrical circuits with caps and coils, the surface of a soap bubble in a metal rod, etc. A sibling is the z-transform, which is like the digital version. This one is used for instance to design digital audio filters. I'm sure some math wizards here can elaborate and correct me.