Only one person can know a private key, but a public key is not secret.
A message encrypted with a public key can only be decrypted with a private key. This means that by using the public key of someone, I can send a message to him, without anyone else being able to read the message.
A secure communication between two people can happen if each one of them has its own private key and the public key of the other.
A second advantage of private and public keys is digital signature. A specific software can hash a message into a message digest, which is then encrypted with our private key. Anyone else is able to verify that we are the author of the message, by using our public key. Then, after obtaining the hash can also verify that the message hasn't been altered.
But how to guarantee that the public key is mine and not a fake one?
For this reason there are certificate authorities! A certificate is created by the authority by digitally signing my public key and information about me. The authority is trusted and there are no doubts about the autenticity of their public key, which is pre-installed into the browser. In that way the recipient of my message can first verify the authenticity of my public key and then the authenticity of my message.
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