So - I understand that description is a bit rough and perhaps hard to follow - but the idea is this:
A high initiative leader like a Guderian or a Patton have an initiative value of 4. Poor leaders, like early French and Russian leaders have an initiative value of 1.
So, what players do is draw (blind) a chit - that is numbered 0-4 on its flip side. Players can move leaders and the units with them that have an initiative value of the chit drawn or higher.
So, a 4 initiative leader has a lot of flexibility - since he can move on any chit draw, he can either move first in a turn or wait to see how things develop and move last. 1 initiative leaders have less flexibility and have to move either on a 0 or a 1 chit. units without army leaders can only move on the 0 (all move) chit.
This makes for very interesting play.
Once all the chits are drawn, players resolve combats. So there is really only on mega turn of movement and combat every game turn, not an Allied turn and an Axis turn - it is all done at the same time.