Video games create space in which to play. Open World games offer a space that is very large, and possibly unlimited. As opposed to games that funnel your movement in a particular direction to create a directed experience, Open World games let you wander in any direction.
These games populate their open worlds with architecture, characters, quests, items and discoveries. The appeal of these games is that when a particularly exciting moment of play occurs it hasn't been pre-ordained by the developer but has emerged from the interactions of the player with the game world.
Open World games come in many forms. Adventures and Role-Playing in large open spaces invite exploration and create a sense of grandeur. Simulation games that offer large explorable worlds offer a chance to experiment with how the games physics, political, economic or even religious models work at scale. Strategy games played in Open Worlds are a chance to innovate techniques that take advantage of the landscape and terrain in which you find yourself.