I'm interested in 'cutting the cord' to digital ("cable") TV service, so I'm exploring the "online" options, such as streaming through my Apple TV (3rd Gen.). I notice that usually when I try to do that, it requires me to visit activate.somewhere.com or otherwise sign in with my TV Provider credentials. What is this all about? And what happens when I don't have a "TV Provider" any more? Will this still work if Verizon (or someone else) still provides only my Internet service? Much thanks.
It's just a place where Apple lets you enter one account and then many apps can use that single sign on to validate you're paying for paid content. This feature is implemented on iOS and tvOS currently.
It's up to each third party app to use the service / API - but in the US this works amazingly well. Many people use it to cut the cord and pay nothing for cable or television packages. You simply pay one of many providers and choose the one you wish to use most and enter it in the OS.
I expect we'll have more news about this within a week (Apple Special Event Live from the Steve Jobs Theater in Cupertino. March 25, 2019, at 10:00 a.m.) and you'll need to read up on your internet provider to see to what degree they implement network neutrality. Some network providers filter / block / charge extra for streaming data - others don't care what bits you download or from where those bits originate. Most providers are somewhere in the middle - throttles and caps, but for most cases you can use this without any added costs or hassle.