Formations are an important aspect of battle gameplay. They are formed by officers, standard bearers, and (optionally) drummers by European factions and by chiefs and shamans by Native American factions.
There are three formation shapes: line, square, and column. Lines are just as they sound; they are most useful when fighting a mass of enemies directly ahead. Squares are hollow rectangle formations; they are useful when surronded by enemies. Columns are like lines but facing the side; they are good for combatting enemies from two opposite sides. Cavalry can also form wedges, triangles good for 'wedging' into a focused area of the enemy line.
The size of a formation can vary. The smallest formation size is 15. Next is 36. Then 72, etc. These numbers do not include officers, chiefs, standard bearers, shamans, or drummers.
The main purposes of formations are to prevent troops from routing quickly and to keep things organized.