In each phase of the turn, one player or the other will have the Initiative. This is important because it determines which player will act first in the events of that phase — which can be a crucial advantage.
The player with the Initiative goes first, or gets to choose who goes first, depending on the phase.
To determine who has the Initiative we draw an Initiative counter from a mug (or another receptacle, such as a small cloth bag):
In the Start phase of each turn, place five Initiative counters in the mug — three for the player whose army has the higher Strategy Rating, and two for the player whose army has the lower Strategy Rating.  
Where the turn sequence instructs you to "Determine the Initiative", one player must draw a random counter from the mug. The player whose counter is drawn has the Initiative.
That player has the Initiative until the next "Determine the Initiative" step in the turn — at which point they may get the Initiative again, or the opposing player may get it, depending upon what counter is drawn.
Do not put the counters back into the mug until the next Start phase.