My grandfather in the USA had webtv for many years. Basically he had been averse to getting a real computer because he was completely unfamiliar with using them and was intimidated by them, and webtv was marketed to people like him as a way to more easily use the internet and send e-mails to your family without needing to learn how to navigate windows or mac operating systems.
Fundamentally, it was like a dumbed down internet browser. The overall experience was very comparable to using planetweb on your dreamcast. It allowed you to browse the internet on your TV with the included keyboard, but you couldn't do stuff like downloading large files since there was no HDD in the webtv unit. I wouldn't be surprised if the webtv disc for dreamcast is a re-skinned sega browser, the functionality that I experienced with webtv (a simple web browser on your tv) would have been very similar to the existing dreamcast browsers and I'd expect the dreamcast webtv software to be the same.