Marching at the double allows troops that are away from the main fighting zones to move more rapidly. This represents the swift movement of reserves by means of a rapid march, and helps to ensure that units don't get stranded away from the fighting.
Marching troops move at twice their normal movement rate with weapons sheathed or shouldered. They are literally going at the double'. A unit on the march is not prepared for combat so marching is not suitable for use close to the enemy. In reality no troops would approach the enemy with weapons unready.
Troops can march if there are no enemy models within 8" at the start of the turn. If there are enemy models within 8" at the start of the turn the unit is busy preparing to fight and so cannot march. Note that the marching unit can move closer than 8" to an enemy as it moves.
A unit on the march cannot change formation or turn as this would disrupt its movement. It can wheel as normal, as you might imagine a column of troops would do in order to follow a route or path, for example. A marching unit cannot move through difficult or other obstructive terrain or cross obstacles. It must stop if it comes to these features.
A unit on the march cannot shoot missile weapons during the shooting phase. It is unprepared for combat and any weapons carried are not ready to be used.