An antinode occurs at the open end of an organ pipe due to the relationship between displacement and pressure in standing waves. At the open end, there is a displacement antinode, allowing maximum particle movement, while simultaneously creating a pressure node since gas can freely move in and out. This means that at the open end, there is no pressure buildup, as the gas is unconfined. Understanding this concept is crucial for grasping the behavior of sound waves in organ pipes. The dynamics of particle movement and pressure distribution are key to this phenomenon.