When a character is faced with a creature that should have them running away or cowering in fear (or which could at least finish them off with one bite) but instead engages it — maybe even beats it — in an impromptu Staring Contest. Picture the scene: Bob The Hero has been cornered by the villain. The Sealed Evil in a Can is about to be unleashed, probably in the form of an Eldritch Abomination. The villain is locking the hero in a Cool Gate to Another Dimension with no chance of return. The Gladiator Games have commenced and it's one unarmed, wounded person against a whole pride of hungry lions. There's nothing anyone can do. There's no backup, no escape, no Big Damn Heroes. All is lost. The world is undone. The lions are going to eat good tonight. HE COMES.
And in the other corner, we see Bob, alone and defenseless, seconds away from complete and utter doom, standing with his eyes fixed directly on what's going to kill him. He stares straight ahead, unaffected, unafraid; at the hungry lions, at the Evil Overlord, even at that hideous, inhuman THING.
The seconds tick by. The forces of evil start to squirm a little bit. The lions don't move in for the kill. The villain's insane cackling falters. HE... HESITATES. The hero, through sheer badassery, has held off something which could have swallowed him in one bite.
Where the situation goes from here depends. Perhaps the bad guy turns tail and runs away. Maybe Bob's staredown has distracted the villain long enough for The Cavalry to charge or the Big Damn Heroes to show up. If the mighty being has to respect Bob's moxie, then you've transitioned into Wowing Cthulhu. Or maybe the villain gets over it and kills the hero after all, but they — and the audience — will always remember that Bob died on his feet and never cowered.
Overlaps with Death Glare and is often portrayed as a Kubrick Stare. The Slow Walk is optional. A hero who goes out staring down and intimidating his killer is always a good candidate for a Dying Moment of Awesome.