Basically, in public key cryptography, you can generate two sets of numbers that are mathematically related, one called the private key and one called the public key, collectively called a key pair.

Through a lot of fancy math, you, with your private key, can take a number I give you and give me back another number called a signature. I, with your public key, can do even more fancy math to prove that you do, in fact, have the corresponding private key to the public key I have based on this signature.

If you give me the wrong signature, I can’t trust that you have the private key, and you don’t get authenticated, but if you give me the right signature, I can trust that you’re you, and you get authenticated.