What are the private and public keys associated with an Apple Distribution Certificate? I'm following this guide on how to generate a new Apple Distribution Certificate, and on the ‘Download your certificate’ page it says

Download your certificate to your Mac, then double click the .cer file to install in Keychain Access. Make sure to save a backup copy of your private and public keys somewhere secure.

What are these private and public keys? Are they contained in the certificate? When I download the certificate and Get Info, it has information about a public key but not a private one.
The certificate contains a copy of the public key. Having the certificate without the private key is meaningless in terms of distributing iOS programs.
The private key is created automatically when you create the certificate signing request as described by the linked to guide. The private key is stored on your local computer, and can be found in the Keychain program.
The private key is not contained in the certificate nor it is not downloadable from Apple's developer web site. You will want to keep the private key, well, private - and secure.