That ID number is public and allows government & any companies/organisations you show it to immediately verify that they are dealing with a specific person, instead of having to spend time figuring out which specific person named "John Smith" they are dealing with. Having this number simply makes life more quicker and convinient. It also allows to remove any pointless duplications for cards.
For some examples: separate medical insurance card was discontinued, you can verify medical coverage by a simple number query. Same with drivers licences, they still exist in a separate physical forms for foreign trips, but but not inside the country. There is no separate libary cards, I don´t have to carry a separate card for my gym or various retailers.
I can verify myself online quickly and securely. I can digitally sign documents and contracts and email them. Honestly, I´m having hard time imagining my life without it. I´m aware that all proposals for national identification methods in the US have failed thanks to fears of "mark of the beast" and big brother, but it seems pretty silly to me. All that data already exists and can be cross referenced. Making average person waste more time and money by having such massive inefficiencies in the system seems rather silly in these times.