Castle is the most important building and a center of your city in the game.
Basically the Castle building performs as a Town Hall - other buildings will unlock as you upgrade your Castle to higher levels.
Upgrading your Castle will also increase your Troop March Capacity as well as your Total Power. You can check out your currently active buff effects by tapping on the Castle buildingCastle Buff.
There is a special Level Reward awaiting for you after each level-up.
Once your Castle reaches level 2, you will be able to choose a direction for you civilization's development (East or West).
Then, upon reaching level 12, you will have to choose a specific nation within the selected civilization (England, Rome, Egypt or Islamic Empire for West; Korea, China, India or Japan for East).
More on types of civilizations in this article.
The outlook of your Castle will vary greatly depending on the civilization and nation you have chosen, as well as its level.
Here is one of a mid-level account of Islamic Empire:
Through the Emblem tab you can access Emblem menu that works for all of your owned buildings.
Emblems are another way of boosting production and/or speeding up processes in selected buildings. Each Emblem's specific effect is displayed in the relevant menu - just tap on a type of Emblem you wish to check.