An intrinsic equation is like a special code that describes a shape or a path in a special way. It's like writing down the instructions for how to draw a picture, but you don't need any other information like how big the paper is or how you're holding your pencil. Everything you need to know is included in the code.
It's kind of like when you play a game and you have to follow the rules exactly as they're written in order to win. With an intrinsic equation, you have to follow the instructions exactly in order to draw the picture or plot the path correctly.
Think of it like a secret language that only some people know how to speak. If you know the language, you can use the intrinsic equation to create amazing things like 3D models of buildings or sculptures. But if you don't know the language, it might sound like gibberish!