1) An entrance or appearance that usually results in the damage or destruction of nearby scenery.
2) An intrusion on a conversation that completely kills it and creates an atmosphere of awkwardness.
Comes from the movie Hancock, where the main character, a superhero, made most of his entrances in the first half of the movie by slamming down on the ground from a high altitude, damaging the pavement and nearby property.
By accidentally driving her car into the convenience store, the old lady did a textbook Hancock Entrance
A Hancock Entrance in conversation
Guy 1: Dude, did you see the baseball game yesterday?
Guy 2: Yeah! It was total bullshit. The shortstop missed the ball to make the last out!
Guy 1: I saw that. The thing went right between his legs
Guy 3: Your mom's thing went right between his legs!