Okay kiddo, have you ever played a game where you have to guess a number and someone tells you if you're "hot" or "cold" depending on how close your guess is to the real number? Well, scientists are kind of like that when it comes to guessing how big numbers can get.
The Chu-Harrington limit is basically like the "hottest" point scientists have gotten to in this guessing game so far. They were trying to figure out how big a number had to be in order for another special number guessing game called "Rado's graph" to happen.
Rado's graph is a fancy way of drawing lines between points, and the scientists wanted to know how many points they needed in order to draw all the lines in this special way. The Chu-Harrington limit tells us that you need a LOT of points (in fact, more than we can even imagine or write down!) in order for all the lines to be drawn correctly in Rado's graph.
It's kind of like saying you need a LOT of legos in order to build a super tall tower - more than you can even count with your fingers and toes! Scientists are always trying to guess how big things can get, and the Chu-Harrington limit is just one of those guesses that helps them learn more about the world around us.