A valve box is an enclosure designed to provide a safe environment for the components that comprise an irrigation system. It protects them from vandalism, the elements and damage due to mowers, string trimmers, etc. An irrigation system is typically divided into several zones, each of which feeds sprinkler heads in a different area of the lawn or garden, and each zone is controlled by a valve that receives signals from a centrally located controller.
When it comes to housing the valves, manifolds, wiring etc., you can choose to put them uncovered in a hole in the ground or use an underground valve box, unless you are installing anti-siphon valves. These have to be installed above ground.