Our Roku is connected to our WiFi. Then we connect it to our TV with an HDMI cable (like a DVD player or gaming system) (As PP stated, no computer involved)
We have subscriptions to Netflix and
Amazon Prime, so we can stream movies from those places
We also stream
YouTube and Pandora quite a bit
Roku also has some free "channels" and access to a lot of other paid for channels like Hulu, RedBox, etc.
We also have the UFC channel so we can get pay-per-view UFC (we have to pay just like Dish or cable, though)...so you can often find a way to get pay-per-view sports
Our Roku also came with Angry Birds
We don't have cable. We have WiFi, Roku, lots of DVDs, and a good antenna. We can get most local stations with the antenna.
We don't really miss cable. DH misses his 24-hour news stations (but he just reads the news on the internet now). The only people I see complain are sports fanatics because you really need cable to get all the games.
We are Droid/Kindle/PC users, so we didn't do AppleTV
We did stream to our TV using our BluRay player and Netflix, but Roku allowed us to stream Amazon, Pandora, YouTube, UFC PPV, etc. that our BluRay couldn't