These are simply larger collections of elements that can move together for the price of moving one unit. They also help protect their comrades once the enemy is engaged. Of course, this increased efficiency of movement has a price. Groups are a lot less maneuverable than single elements. As an example, the groups can only move forward or pivot in a forward direction.
Elements can back up or slide horizontally.
However, being able to move many units for the price of one has its advantages. Movement distances of course vary with terrain. The movement system took me a little bit of getting used to. With elements you have several buttons off in the right hand bar that control how you are moving. With one of them highlighted you are on rotation mode.