How do you describe to kids what can we archive with programming?

Fun is subjective. People often don't believe when being told something is fun. It's easier to make the description itself fun, though it will backfire if the process of programming itself turns out not to be fun.

Start out with Hello World and some math problems. Then make forums where they can change colors and make animations and stuff like that. Make simple video games to keep them challenged and show them what they can do.

Archive, I think you mean achieve?

How old are the kids?