"Anything" usually means more than nothing. Can you see anything? No, my eyes are closed.
"Everything" means "all things" or "every thing". "Everything in this store costs less than $20."
No one would say that you can see "everything" with a telescope.
Here's where the joke is: Sometimes, (and it's confusing) "anything" can mean "any thing that you want". For example, an ad might say: "With this tool, you can do ANYTHING!"
So the child is asking "can you see anything with that telescope." The father thinks he means "more than nothing." So he says, "of course." But the child was asking "can you see anything you want to see?" So when the father says yes, Jack asks whether the father can see his kite.