Let's start with a smartphone. A user creates an account with a passkey for a service, that passkey gets stored on their smartphone, and they can use biometrics to sign in from then on. The private key is stored on the smartphone. Great.
But then how do you sign into that same service from a different device?
If it's by using a password manager, some third party piece of software, How do you sign in on a device where you're not allowed to install third party software?
Depending on the site, you can use one device to login to another without installing additional software. For instance, if you have an iPhone with a passkey for microsoft.com stored on it, you can login to Microsoft.com using the iPhone.
Here is a webpage that has some screenshots to show you what I mean. You can probably google some other examples.