Can you explain RSA encryption keys in simple enough language for me?

I’ve read about RSA encryption, public and private keys, and Diffie-Hellman again and again, and I’m still having trouble with the concept.

One of the things that slow me down is the public vs. private key part. If you have a private key, what do you want a public key for? What’s the point of using a lock anybody can pick along with a lock to which there’s literally only one key? Why bother with the public key at all?

To make it simple enough for me, you’ll probably have to use an analogy or metaphor. Never mind a mathematical formula; they just hit my blind spot.