Movement is clearly vital to the game - as the armies have to get close to each other to inflict damage and therefore win. How and where you move your troops is therefore vitally important. Moving them haphazardly and without thought as to what your opponent could do will soon place your army in jeopardy.
The basic rules are these. That some troops (such as heavy foot) move more slowly than others (such as light cavalry). This reflects the fact that such troops are weighed down by armour, heavy spears and the like which slows them down. The movement rates are shown below.
Heavy Foot - 3MU
Medium Foot - 4MU
Light Foot - 5MU
Heavy cavalry - 4MU
Cavalry - 5MU
Light Horse - 7MU
So on the battlefield, Light Foot can easily evade heavy foot (which are dependent on melee weapons to inflict damage). Similarly Light Horse can evade Heavy Cavalry - and can move more than twice the distance that Heavy Foot can. So a drilled Light Horse BG could easily outflank or get behind an undrilled heavy foot BG in a couple of moves (the undrilled BG finding it difficult to execute a 180 degree move to face the horse means being contacted in the flank or rear at -PoA).
This use of variable movement is important. FOG rarely involves two armies walking towards each other and clashing in the middle of the battlefield. Commanders instead aim to use the movement abilities of their troops to effect an advantage.
In addition, some troops are better at undertaking complex moves than others. So a Drilled unit is more able to move around in complex formations than Undrilled. The distinction may not be apparent initially, but this ability can significantly affect combats.