Movies that make you feel something. Sure it's a nebulous qualifier, but watch any of these films and you'll understand why they're recommended as movies that won't leave you with that numb feeling of having sat through a movie that didn't really do anything for you.
If you've never seen Grave of the Fireflies, it's an absolutely beautiful animated movie that will leave you devastated at the end. However, not every film that makes you feel something emotional has to be sad. Other movies like Inception or Interstellar might make you feel awestruck, amazed, or perhaps even inspired.
The best movies to make you feel something are often dramas or character studies (or both). These types of films allow us to connect with characters on an emotional level and experience their struggles as if they were our own. When done well, these types of films can be truly life-changing experiences for viewers - which is why they're often called "movies that change your life."