In addition to on-demand programming like TV series and movies, Showtime allows you to watch live video, showing you what's currently running on Showtime East and Showtime West. You can also see a schedule of upcoming movies and series.
The service comes with a 30-day free trial to let you test the service out. Following the trial, Showtime will cost you $10.99 per month, less than what competing service HBO Now will run you.
You should find Showtime sitting on your home screen the next time you turn on your Apple TV.