@NajibIdrissi I first heard of operads from the following paper by John Baez: arxiv.org/abs/q-alg/9705009 They show up about halfway through. Not genuinely grasping the concept, I looked for another source and came up with The Geometry of Iterated Loop Spaces by JP May. While I can grasp the definitions in each formally, I just have a hard time understanding what they are meant to model and how. In the same way that a topological space is a set with a topology on it meant to model a space or shape (roughly), what are operads meant to model through their formal definition?

I wish I could be more concrete about the type of operads I am referring to. I assume "regular" operads are what I am referring to, given I am only now learning about them. But thank you for the links, everyone.