What is Lambda Calculus and why?

I was going to make it nicer but I ran out of patience. And time. But mostly patience. But hey, production quality is not important, right? Pencil Code demo: http://yanamal.pencilcode.net/edit/functions Lambda Calculus visualizer repository (warning: the text is currently wrong and the code is janky): https://github.com/yanamal/lambda-js