Marching troops move at twice their normal Movement rate with weapons sheathed or shouldered. They are literally 'going at the double'. A unit that is on the march is not prepared for combat so marching is not suitable for a unit that is close to the enemy. In reality, no troops would approach the enemy with their weapons unready to defend or attack with.
Troops can march if there are no enemy models within 8" of them at the start of the turn. If there are enemy models (fleeing enemies do not count) anywhere within 8" at the start of the turn, the unit is too 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 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 that is on the march cannot shoot missile weapons during the Shooting phase. It is unprepared for combat and any weapons it carries are not ready to be used. Any Wizards with the unit can still cast spells.