My new router is a Linksys Max-Stream AC1900 MU-MIMO gigabit router.

The modem is an Arris SURFboard 660 series - SB6183.

In my case they are two separate devices, because the old Comcast cable modem was just a modem, not a combination modem + router, and I did not replace the router at the same time as the modem.

Roku is an internet streaming device to watch things from the internet on your TV. Apple TV, Google Chromecast and Amazon Fire are similar devices. Gaming devices like Playstation and some DVRs also have the ability to stream to your TV. Newer TVs come with internet streaming ability built-in, but my 9-year-old TV is otherwise working well so I saw no need to replace it. I could connect a laptop to my TV in order to livestream to it, but the Roku (or Apple TV, etc) is more convenient. I think a lot of people use streaming devices to watch shows and movies from services like Netflix and Amazon Prime even if they also have cable TV. But it seems to be increasingly easier to get rid of cable and still watch lots of shows online, either on demand or in real time, which is what I'm trying to do.

BTW last week I got an email from Playstation Vue telling me they are raising their rates. I currently have the base channels + sports + movies, so if I stay with them I will drop down to just base channels + sports. I'm going to try DirecTV Now next to see if I like their interface better. They don't have a cloud DVR but I most of the things I would want to record would be available on demand. Part of this process for me is getting used to the whole on demand thing, which I never really needed to use with the cable TV.