Robber Baron Castles (commonly called RBC's) randomly spawn on the map. They only increase level (to you only) if you attack them, They often drop equipment when level 3 or above. Often, if you spy on one, all RBC's with the same level will have that exact same troop formation. Robber Baron Castles may sometimes attack players. These can also give out rubies (when above level 3) as well as Time Skips.
The image on the right shows the stats of the battle. The number of troops brought into battle, the number lost, and the same for the defenders as well. It also shows the XP you got, the honor (which will always be zero), and the number in the hospital. Below the XP and hospitalized troops (which you can click to heal or kill the troops) is detailed info on how you can better do the battle (better troops? zeroing out all the tools? working on combat strength?) the next time you face the same castle. On the right, it shows the piece of Equipment or a Gem you earned (which goes to the inventory immediately and also a time skip earned. Further to the right, it shows the loot earned in battle, with wood and food on the top, and the coins and stone on the bottom. If you are level 70, you can also collect Iron ore (or the kingdom equivalent in other kingdoms before level 70).