These are possibly the most important aspect of the game ranking number two just under food production.
When you open one there is a tab at the bottom that will show you specific details about that battle. On that section you can click the button on the bottom again to forward it to your whole alliance or specific players. This is important to do, at least to the leadership of your alliance.
On the detailed section there are two important symbols. One is a skull. This is your troops details. It tells you how many of what kind survived and which got destroyed. It tells you what kind of troops they all fought against in the opposite tabs. The second symbol is a scaling ladder. This dominates the tools used on both sides. You get a precise comparison of what you used and what you beat from the opposite colomn. These details are very important to planning good battle strategy in future battles.
On here you can also see who was the attacker and who was the defender, in other words who got attacked. You can see this in the main overview that you see when you first open the report and also on the overview page of the detailed report. Click on the icon of the attacker and you can go directly to his or her castle from there. You can also see the name of the player who did it so you know exactly who attacked you. If you choose to go to the castle of the attacker, you can see all of the player details, including which alliance that they are from.
This is why sending battle reports to your leaders of your alliance is so important.
When a player gets attacked by another player it usually causes alliance wars. This falls into diplomacy and diplomacy is the responsibility of the leadership and cannot be avoided. If your leaders are in the dark on important battle details in the report when a player doesn't send one, then they have no tools for diplomacy and diplomacy can't really happen on the level it needs to to reach an agreement to end the war or handle negotiations.
In my alliance if you fail to send important player attack battle reports it's cause to kick you out of my alliance. As I've said in other posts, I run a no hit players alliance and my members are happy in it. You can enjoy the game with all of it's benefits in a fair way to all involved.