The credits for 3-Iron say that our breaking-and-entering protagonist is named Tae-suk (Hee Jae), though I don't recall ever learning his name in the film itself. We learn little that's concrete about Tae-suk, save that he's obviously lonely and disaffected. His grooming, attire and expensive motorcycle would suggest that he is neither poor nor conventionally desperate, but we are told nothing of his family or education. His haunted eyes suggest that he's alienated from the commonplace world and yearning for a connection he's never made. He's looking for something spiritually elusive, absent from his own life, something that perhaps resides in the homes he invades. Perhaps that something is represented in the physical form of the gorgeous, ethereal model whose photograph seems to hang on so many walls.
Tae-suk's standard routine is disrupted one day when a home he's entered has a coffee-table book of photographs of that beautiful model, many of them tastefully posed nudes. He disrobes and slides into a bed, book in hand, to masturbate. Only this time he's broken into the model's own house Ñ and she's home. And she's been beaten up by her vicious husband. Things turn ominous when the husband returns unexpectedly and, not realizing Tae-suk's presence, begins to abuse his wife anew.
We expect Tae-suk to defend the woman, whose name the credits identify as Sun-hwa (Seung-yeon Lee), and he does. But here is where an already odd movie, to this point almost utterly devoid of dialogue, leaps into a realm other than our own. The husband (Hyuk-ho Kwon) yells at the wife as he smacks her, but she does not respond. And Tae-suk utters no sound in intervening. Rather, Tae-suk fetches the husband's treasured 3-iron, drops a few golf balls at his feet and begins to rifle line drives into the husband's body. Shortly, the husband is bruised and defeated, curled into a fetal ball of pain. Communicating only with his eyes, Tae-suk offers Sun-hwa a spot on the rear of his motorcycle, and they are off.
Together they take up the routines of Tae-suk's life. They distribute flyers, identify what they think are empty houses, make love in borrowed beds and do the laundry and fix the broken appliances of strangers. What they don't do is ever speak a single word. In daylight hours, Tae-suk will often practice 3-iron shots with a device he has fashioned by attaching a golf ball to a length of cord he wraps around trees. When Sun-hwa grows impatient with his practice, she gets him to stop, not by asking, but by standing in front of him so that he can't swing his club without hitting her.
Then in a development I can't quite account for, they gradually target less and less affluent residences until they finally enter a small apartment where an old man has recently died in the kitchen. The service they provide this time is to wash the corpse, gently wrap it in a ceremonial shroud and give it a dignified burial. And then they are busted when the distraught family of the deceased arrives to accuse them of murder. They don't protest their innocence, of course, because they don't speak. And then this strange movie becomes stranger still. Responding to his brutalization in prison, Tae-suk begins to practice a kind of anti-martial arts regimen that makes him not just impossible to hit, but even to see. Invisible, he escapes from prison and returns to Sun-hwa, the only person to whom he needs to reveal himself.
Director Kim provides a caption for this visual poem of a movie. It reads, "It's hard to tell what's reality and what's a dream." 3-Iron seems to start in reality but end in a dream where events make only metaphorical sense and perhaps not that. While together in one of the houses they've entered, Tae-suk alters a scale so that the lovers register as weightless when standing on it. In the end, we should perhaps understand their union as existing only in the imagination, the sole refuge where they can escape the bonds of a troubled world.