In a langstroth hive a box is where Frames go in. The box keeps the frames at the correct spacing so the bees don’t make a mess. There are two uses of boxes, Brood chambers and honey supers. The Brood chambers are obviously where the bees have their brood and honey supers are where Nectar is stored and made into honey. Boxes can also have different sizes, deeps, mediums, and shallows. Deep boxes are usually used for brood chambers, mediums are usually used for honey supers, and shallows are very uncommon.
The brood chamber is a deep box here while the honey super is a medium. See Hive Parts for more details on this entire subject or click a link here to find out more about a specific part: Outer Cover (specifically a telescoping top in this picture), Hive topper/Vent box, Inner Cover, Bottom Board (specifically a screen bottom board in this picture).