Bitwarden (as an example) allows you to store your TOTP tokens in it. That is: you can use the mobile app to scan the QR code that (e.g.) Amazon AWS gives you, and then it'll generate TOTP codes.
So far, so exactly the same as Google Authenticator and similar.
Bitwarden synchronises your "vault" (to their servers by default; you can install your own server), including the TOTP ... stuff. This means that your credentials (including TOTP codes) are available on all of your associated devices.
Is that a good thing, from a security point of view? It's definitely convenient -- I just got a new phone, and resetting all of my MFA tokens is ... not a pleasant use of my time.