Zero gravity or null gravity is the natural freefall environment of space, where there's the illusion of weightlessness despite the surrounding objects still exert gravitational force.
The command module of the Ares IV, an Earth spaceship, had a zero gravity environment. (VOY: "One Small Step")
By 2151, artificial gravity had been invented to counter zero gravity. However, every ship still had an area where zero gravity was maintained. Travis Mayweather called the area the "sweet spot" during his youth aboard the ECS Horizon. (ENT: "Broken Bow")
A location aboard the ECS Fortunate was intentionally kept in a zero, or low, gravity environment. There, members of the crew could throw a baseball through the low gravity area while standing in an artificial gravity zone. (ENT: "Fortunate Son")
Although artificial gravity was usually maintained in most sections of a starship, a vessel's environment can revert to its natural zero gravity state when its artificial gravity systems fail.
Background
A jar which didnt appeared in the NX-class sickbay in Star Trek: Enterprise and which was sold off on the It's A Wrap! sale and auction on eBay has the label Do not store under null gravity condition. [1]