Its a cryptographic way of verifying something without having to expose the information it's verifying.

Lets say you need to prove you're over the age of 18

You can have a digital ID that has your birthdate on it.

Through some fancy cryptographic stuff I can't explain, the website could challenge your ID to prove your age, and the ID could return a response that proves you are over 18, but it doesn't need to actually give your name or age in response, and it's response isn't something that can be linked back to your ID.

Now simply having an ID isn't necessarily enough, kids could just take someones ID, so it might need to have some biometic's added and be a small piece of hardware that has the digital ID, so when the website challenges the ID, you unlock the ID with your fingerprint, and now the website knows the owner of that ID is the user of the ID, and they are 18 or older.

For this to work though you'd need someone who has authority on your age to implement the digital ID properly, and then write the software that will validate things.

So you could go to the DMV as an example, they issue you a license while you're there, you authenticate the ID with your finger print (but they DMV doesn't get your fingerprint, it's just stored on the ID) and then the website can challenge the ID and get a response that verifies you're old enough, without verifying who you are, or your age.

Edit: just to add, and ID like this wouldn't be limited to online. You could go to the liquor store and validate without them having to see your ID which exposes where you live for example.