Short answers, pulled from the story.
In Metal Gear Solid, Psycho Mantis reads the player's memory card and has special responses for saves from Castlevania: Symphony of the Night, Suikoden, Azure Dreams, Vandal Hearts, Tokimeki Memorial, and Policenauts. In The Twin Snakes, the 2004 remake, he instead recognizes saves from Super Smash Bros. Melee, Super Mario Sunshine, The Legend of Zelda: The Wind Waker, and Eternal Darkness.
Psycho Mantis reads controller inputs from the first controller port, allowing him to dodge every attack. Players defeat him by moving their controller from port 1 to port 2, cutting off his ability to read their movements. Snake then kills him in the battle that follows.
Doug Stone voiced Psycho Mantis in English and Kazuyuki Sogabe voiced him in Japanese. Stone later reprised his English role in a 2016 Ford Focus advertisement that parodied the Psycho Mantis encounter.
Hideo Kojima was inspired to create Psycho Mantis after watching the 1978 film The Fury, which the development team used as a reference for depicting psychic power. Kojima wanted to express the concept of a master telling a student to clear their mind. The controller port switch was the only method he could find to express that idea in a video game.
Psycho Mantis appears in several later Metal Gear games. His ghost controls the body of Screaming Mantis in Metal Gear Solid 4: Guns of the Patriots, and a younger version called the Third Child appears in Metal Gear Solid V: The Phantom Pain, where antagonist Skull Face uses him to control a Metal Gear mech. He also makes cameo appearances in Metal Gear Solid V: Ground Zeroes and in the 2024 game Astro Bot.
Critics and academics consistently call the Psycho Mantis encounter one of the most iconic moments in video game history. Mantis broke the fourth wall by reading the player's save data, manipulating their physical controller, and requiring real-world action to defeat him. Academics describe the battle as generating genuine confusion between player identity and game character, an experience noted as not replicable outside of Metal Gear Solid itself.