Here's how it works:
You set up a "quorum" which is a number of Yubikeys required to access the root private key. For example, you may need 2 of the 3 total Yubikeys to reach quorum.
Using the shard stored on your mobile device, you will generate an encrypted file containing your portfolio root private key.
You can then use the encrypted file and your security keys, without Coinbase's involvement, to extract and access the root private key.
Once you have the root private key, you can transact without Coinbase by, for example, importing your key into another non-custodial wallet.
For more information regarding Export Onchain Key, please view the PDF guide within the Prime platform that can be downloaded here:
Warnings on Key Export risks
Exporting your onchain keys means that your private key can be accessed independently of Coinbase, therefore you need to ensure that your exported backup is stored securely.
Private key theft: Without proper security for your encrypted backup file and YubiKeys, an insider could potentially steal/access your private key.
Loss of access to your exported backup: If you lose the backup file or don't have enough YubiKeys to meet the "quorum" threshold, you will lose access to your exported backup. If you still have access to a valid provisioned device (or recovery phrase) for your Prime Onchain Wallet, it is possible to recreate the quorum of YubiKeys and export a new encrypted backup.