Can anyone explain to me how pirating and torrenting works?

I do not intend to break any of the rules for this subreddit (please correct me so). I want to know, in simple terms, how torrenting and pirating really works. I have been "legally" buying games, movies, and music for years now, and I realized that my wallet isn't exactly up for my shopping sprees. So if you could direct me to some SAFE websites for torrenting, that would be great (but I want to know how that works).