Okay, so imagine you're playing with your toys and there are different groups of toys. In 2003, some toy soldiers from one big group (the United States) went to another group's area (Iraq) to fight because they thought the other group had bad guy toys (weapons of mass destruction).
Before they went, the United States made a list of all the toy soldiers they would bring and what they would do. This list is called the "order of battle." Just like how you might make a list of which toys you want to bring to a friend's house to play with.
The United States also had help from other countries who sent their own toy soldiers to fight. So the order of battle listed not only the American soldiers, but also soldiers from other countries and what they would do in the fight.
The order of battle helped the United States plan out their fighting strategy and make sure they were prepared to take on the other group's toys. They wanted to make sure they could protect themselves and their friends who also didn't want the other group's toys to harm them.