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Don't think it works for logging in (although some versions do).
This is the basic version, works for 2FA for logging into things like Facebook, Google, etc (mine's mainly for getting into google/email if I can't use authy). I think the plan was for it to expand what it worked with but I don't think it's happened yet.
I think this is what it's compatible with
https://www.yubico.com/products/yubikey-hardware/compare-security-key-series/
There's a "better" version that works with lastpass and others which @Velocio uses which does more
https://www.yubico.com/products/yubikey-hardware/compare-yubikeys/
Mine is a cheap version of the security key.
Trying to set up 2FA on FAcebook is a real ballache without giving them your mobile. They insist on 2 methods of 2FA so you can't just use Authy, there also needs to be a secondary option.
I use a USB key, one of these https://www.amazon.co.uk/dp/B01M1R5LRD , but a lot of people must just opt to give them their details.