When you leave things out, you provide openings for your readers to enter your stories. An important example I've offered in the past has been using clues and secrets. Obviously, mysteries rely on these, but they are fundamental to most storytelling because readers like seeing the spaces where they can imagine completing the puzzle.
Another example is loss, especially when it creates a sense of nostalgia. When someone from the future uncovers an artifact from our own time (or one we know well), our knowledge of its context and our ability to understand and regret what has been destroyed makes that moment in the story more personal. The Statue of Liberty at the end of the original Planet of the Apes may be the most famous example, but I still remember when I read Stephen Vincent Benét's By the Waters of Babylon and the main character's discovery of post-apocalypse New York. Philip K. Dick provides examples that indicate a twisted past, as when a character shows off the cigarette lighter Franklin Roosevelt was carrying when he was assassinated.
Irony is a classic way to gain reader participation. When readers have
information, especially contextual information, that the point of view
character does not, the reader is forced into the position of seeing bad
choices and having no way to advise a character with whom he or she
identifies. Movies love to do this, perhaps most famously in those
directed by Hitchcock. In fact, his description of suspense is all about
the audience knowing a bomb is present when the characters don't. The
sort of "Get out! Get out!" reaction is delicious. It's why a lot of
people at horror movies advise characters (often shouting) not open the door the monster
When a historical person is depicted as the opposite of what we expect, that can also create a kind of ironic recognition that puts the reader into a space that's both uncomfortable and familiar. I think part of the appeal of stories that include Nicola Tesla as the hero is the way they challenge myths that Edison was a great benefactor who invented much of the modern world (though the mythos seems to be shifting enough, so the Edison switch may be losing its punch). Taking someone who is part of the contemporary Pantheon, like Einstein or Lincoln or Mark Twain, and exploring their dark sides at a distance through a naïve character who only sees the bad is a (somewhat dangerous) way to get under a reader's skin.
Antiheroes take things further. How can we both want Walter White or Tony Soprano to succeed and be horrified when they do? Certainly, empathy and identification with the protagonist is elegantly established in the best antihero stories. But there's more. The writer must be willing to follow through on the antisocial behaviors, often taking them further than readers or audiences might anticipate. Strangely enough, I believe antiheroes who go too far and evaporate excuses we might make for what they do draw us more deeply into the stories because we are forced to re-create our emotional landscapes.
And, though many readers are offended by ambiguous or bittersweet endings (much less tragedies), these are often among the most memorable. The spinning top at the end of Christopher Nolan's Inception forces audiences to write many endings. And if Rhett Butler had said, after Scarlet's pleading, "Okay, I'll stay," I suspect Gone with the Wind would have lost much of its power and its ability to capture the imaginations of generations of moviegoers.
Suggest things. Leave things out. Create questions. Turn things upside down. Surprise. Startle. Don't be afraid to challenge, discomfort, and even irritate your readers. Purposely create invitations throughout your stories so readers are encouraged to participate and stay engaged.