The digital ID e.g. eID is for example if you want to order a government document online. At the current time you need to print out your request and send a copy of your ID in the mail or go to the counter and show it. Same if you get a bank account or new phone contract although those usually let you scan your ID with your phone. A eID would make that more secure although people are already being tricked into doing face validations[1]...
Offline it would make it possible to verify your age at the self-checkout registers without having someone have to check in person.
In the future (if the law allows it, which it currently does not) it should be possible for you to purchase an item online completely anonymously, at least to the vendor. There would no longer be a possibility of leaked address, etc. as the vendor would not have it. All the vendor has are signed tokens. When they send a package they send it with a token to the post office and only the post office knows your address.
