Lee, "Abo" is short for Abonnement, which literally translates as "subscription" (like for a magazine or club), but it is also used for a ticket that is valid for unlimited journeys for a number of days, weeks or months. These are called "Season tickets" in the UK (see here: https://ojp.nationalrail.co.uk/service/seasonticket/search ).
I don't think a Bahn Card counts as an Abo, as you still need to buy a ticket as well.
I have a Swiss regional Abo which is valid for all transport in and around the city I live in. A similar scheme exists in London, it is called a "travelcard".
A transport "Abo", or a "season ticket" does not automatically renew, newspapers Abo's may well automatically renew.
So far it looks like it is for commuters, who can reserve "their" seat, the same seat on the same train every day.
It also says you have to put in the number of your Abo-ticket to register.
Maybe in a few months they will extend the scheme.