The Kubrick stare is a very specific type of shot composition. It’s only probably useful if you’re making a horror or suspense film. Want to make someone look particularly psychotic? Give the Kubrick stare a shot. Have your actor tilt their head down slightly and stare forward.
This style of shot composition derives its name from director Stanley Kubrick who used the technique in a number of films, including 2001: A Space Odyssey (1968), A Clockwork Orange (1971) and The Shining (1980).
As noted at TV Tropes: “When some other show or film utilizes the look, it’s often a homage to Stanley Kubrick. It generally signifies that the character in question is either really, really pissed or really, really deranged, and the person they’re looking at is really, really screwed. Other times—usually when combined with a smile—it means they’re feeling really, really clever.”
You’ll also notice this technique used in Donnie Darko (2001) and The Dark Knight (2008).