Haze is the fog or mist that's caused by small particles in the air. There is often a haze hovering over the city of Los Angeles.
Although the noun haze can describe any kind of misty or slightly obscured air, it usually refers to visible air pollution, rather than just fog. You can also talk about being in a haze when you're confused or disoriented. When you hear haze being used as a verb, it usually means to torment a new, young recruit to a club, group, team, the way fraternity brothers sometimes haze a new member, forcing him to perform humiliating or dangerous actions.