This is an orthodox cathedral, built in early 1900s on Russian money for the Russian orthodox people who lived in Tallinn. This building dominates the surroundings, but it is actually quite small from the inside. The church is active, so you can go inside and check out the beauty of a typical Russian orthodox church. Tourists like to take pictures of the onion shaped cupolas of the cathedral (some wise man estimated 5 millions of pictures of Cathedral per year), and often forget to pay attention to the Parliament house, which is located just opposite the church.
There are some rules to follow when entering the orthodox church, but tourists are not punished. However, it is not so difficult to follow the rules and pay your respect to the holy place: men must have their hair uncovered, while women must cover their heads. Also, it is not recommended to show too much naked flesh in the church (cover your knees and shoulders).