A passkey is an implementation of public key authentication.
The private part should stay with you, this is your identity. The public part gets shared with others, they can use this to verify your identity. "microsoft passkey" wraps all this up into a simple tool that just looks like you are putting in a pin number.
The vague thousand foot mechanism is. someone who wants to verify your identity will ask you to sign a unique number. because only you have the private part needed to to do this, only you can sign it correctly. they can then use the public part to verify the signature is correct. and know it is really you they are talking to.
The private part is usually protected by a device, something to prevent others from using it. this is often just a password, in this case a PIN. but some times is a dedicated usb dongle. this only has to have local security guarantees not global network security guarantees. so a simple password like a PIN is not considered a problem.
The primary advantage over a simple password based system is that the thing that is shared(the public part) is unable to be used as your identity so it can't be stolen like a password. or perhaps more accurately, it does not matter if the public part is stolen(it is already public knowledge)
And now the irony, I have no proof, however I have a suspicion that because loosing the private part is the same as loosing your identity, that is, a big deal and a huge hassle to recover the account. I suspect microsoft is storing them internally. which means your account security degrades to a password based system where the password is basically pubic knowledge, that is, your so called security questions. what is your favorite color? is not a good password.