I struggled to understand what the author is talking about, and the wikipedia page about lambda calculus only added confusion, but I feel like I sensed the idea

I struggled to understand what the author is talking about, and the wikipedia page about lambda calculus only added confusion, but I feel like I sensed the idea behind it: "by skillfully combining a few basic functions, we can produce any output we like, and by skillfully encoding those skillfully combined functions we can compress any data into a particularly compact program." Is this a good summary?