CertSimple will be shutting down on January 30 2020. Read the announcement here.
By default, the private key is created during the certificate purchase process, just after you entered your company details.
We use a new technology called webcrypto to safely generate properly random keys in the browser.
The file in 'download this file and keep it' is your private key:
If you've lost the private key file, you can easily generate a new keypair and new certificate.