It’s also one of his more moronic quotes. Certainly on a very abstract, dumbed-down level everything can be explained simply; sure, if you cannot give your parents a rough idea what you’re doing, you might want to look into more examples. But there are plenty of things which require a very extensive basis to be understood thoroughly.
For example, it is very easy to summarise what a (mathematical) group is and for anyone with a basic understanding of abstract maths, it will be understandable. It’s also very simple to find some examples (integers with addition, ℝ/{0} with multiplication etc.) which might be understandable by laypeople, but you will either confuse the latter or only give examples and not the actually important content.
Further, when you have “simply explained” what a group is, can you go on and equally “simply explain“ what a the fundamental representation is and how irreducible representations come about? You just need a certain level of knowledge (e.g., linear algebra) already and not every paper can include a full introduction into representation theory.