Instead of having a thing that I know and that you know, and that you know that when I present it that it must be me, I have what's called a key pair. Keys here being very large numbers. And in this case, a key pair where the two very large numbers are mathematically related in a very subtle and indiscernible way. If you start then with this key pair, one of the keys is kept private and one of them is made public. The private key I keep and is mine alone.
Nobody has that.
The public key, as the name implies, is made available to all. So when I want to make my mark, or place my imprimatur on a document or on a message or on anything, I apply my private key. You then, and anybody actually out there in the public or anywhere who has my public key, can use my public key to check that I placed my imprimatur on the document or the message or the issue that is confronting me. So in essence, it is a way for me to make a private mark which then can be publicly verified by anyone. And it does not require the sharing of any secrets between me and the parties with whom I wish to do business.