BitID is a passwordless way to login on a website. Rather than using an email and a password, BitID uses your Ledger Wallet to sign a challenge and identify yourself.
To better understand how it works, the best way is to test it.
Got to http://bitid.bitcoin.blue/ and click on the "Sign me in with my Bitcoin address" button:
Then select the Ledger Wallet tab and click on "Login with your Ledger Wallet" button:
It will open the Ledger Chrome app. Insert your Nano and enter your PIN. Once the wallet is initialized, you will see a login confirmation dialog:
When the signature has been calculated, click on the "Confirm" button and you you'll be logged in on the website!
You can also enter manually a BitID URI by launching BitID directly from apps directory:
If you are curious about how to implement BitID on your website, visit the Github repository.