I'll work on better clarification in the rules.
Re-rolls per round of battle. Ground leaders re-roll on the Ground battle-board, naval leaders on the naval battleboard. no leaders or re-rolls on the air-to-air battleboard (though air leaders may be interesting some day).
For example, Guderian - with two re-rolls - can either re-roll two of his own dice OR make the enemy re-roll two of their dice for every round of battle. A re-roll must be declared immediately after the dice are rolled.
So, let's say Guderian's attack is made up of 2 panzergrenadiers (needing 4s); 4 panzers (needing 6s), 2 artillery (needing 5s) and 2 stukas (needing 6s). The German player decides to roll the 2 panzergrenadiers first, rolling a 3 and a 5. He would have to decide immediately whether he wants to re-roll the 5 or save his re-rolls for later. Lets say he decides to save it and rolls his panzers next (rolling a 4,6,9, and 10). He would have to decide before rolling any other dice whether he wants to re-roll his tanks. He decides again to save his re-rolls. Finally he rolls 2 red dice and 2 white dice for his artillery and stukas (respectively) and misses with all of them. The German player again decided to save his re-rolls and use them to make his opponent re-roll dice.
Guderian is attacking 6 French infantry and 1 french tank unit supported by 2 French Artillery. The French player decides to roll his 2 artillery first, rolling a 3 and a 4. Guderian decided to accept his two losses and takes them off of his panzergrenadiers. The French player next rolls his tank unit and misses. Finally, the French player rolls his 6 infantry and hits only with one. Guderian uses one of his re-rolls to make the French player roll the die that hit. The French player re-rolls a "2" and hits again with his infantry unit. Guderian uses his last re-roll to make the French player re-roll that infantry hit again and this time the French infantry rolls an 8 and misses.
Combat for the round is over. If both sides elect to stay and continue to fight into another round, Guderian would again get 2 re-rolls to use to re-roll his own unit's misses or his opponents hits.