iTunes is a beast with many heads. As an application on your Mac or PC, it acts as a media player, media organizer, CD ripper, online radio broadcaster, mobile device management software. Additionally, the application connects to the iTunes Store to allow you to purchase music, movies, and television shows.
The iTunes Store has past television seasons and episodes available for purchase. Additionally, some shows have a 'Season Pass' available, which allows you to follow along with a TV season that is currently airing on broadcast TV. Episodes are the day after the original broadcast. For example, The Walking Dead airs Sunday nights at 9:00 PM Eastern. The iTunes Store will typically have the episode available to watch by Monday morning at 2:00 AM or so.
iTunes also has movies available to purchase or rent.
Watch on your TV
One of the most convenient ways to purchase and watch iTunes content on your living room TV is on the Apple TV device. These small consoles connect to your TV via HDMI, connect to the Internet via Wi-Fi or Ethernet, and come with a simple remote control. Once content is purchased via iTunes, the Apple TV will allow you to start streaming the content on your TV.
Watch on other devices
You can watch iTunes content on your Windows PC or Mac. Also, Apple mobile devices such as iPhones, iPads, and iPod Touches will all play your content purchased in iTunes.
You cannot watch iTunes content on Android devices or other media devices such as Roku boxes.