Okay kiddo, have you ever played with Lego blocks? Each Lego block is a single piece, but when you put lots of Lego blocks together in a certain way, you can build something bigger, like a model airplane or a castle.
Computers work in a similar way. They have little pieces called binary code that are like Lego blocks. Binary code is just a bunch of 1s and 0s that tell the computer what to do. Just like how different Lego blocks can be put together to build something big, different pieces of binary code can be put together to make computer programs.
Now, sometimes people make updates to computer programs to fix bugs or add new features. But if they change the binary code too much, then the program might not work on certain computers anymore. It's like if you built a Lego airplane out of lots of different colored bricks, but then you took out some of the bricks and replaced them with different colors. The airplane might still look cool, but it might not fly anymore.
So, binary-code compatibility means that when people make updates to computer programs, they try to change as little of the binary code as possible so that the program will still work on lots of different computers. It's like if you built a Lego airplane out of red and blue bricks, and you wanted to add some yellow bricks to make it look nicer. You could add some yellow bricks without taking out any of the red or blue bricks, and the airplane would still fly just fine.
So binary-code compatibility is important because it allows computer programs to work on lots of different types of computers without having to rewrite the whole program every time there's an update. Just like how Lego blocks can be used to build many different things, binary code can be used to create lots of different computer programs, as long as they're compatible with each other.