Can someone explain Gödel's incompleteness theorem and Turing's halting problem undecidability proof in different terms or with some simple analogies? Every time I feel like I might understand them, I later realize I don't really think I do.

Can someone explain Gödel's incompleteness theorem and Turing's halting problem undecidability proof in different terms or with some simple analogies? Every time I feel like I might understand them, I later realize I don't really think I do.