Why is cultural understanding important to leaders?

The last thing you want to do as a leader is to offend one of your subordinates by lack of knowledge of their culture. Cultural understanding makes you the ideal candidate for anyone in your group to come talk to about any problem. You definitely do not want ethnic cliques to form in your group, because it only leads to lack of listening and surplus of conflict.
Another fault of not being culturally understanding is the tension that arises. Different ethnic groups have tension between each other because they are not knowledgeable and feel safer talking to people who look like them and who they deem to be more culturally understanding.
This creates a lot of dissonance in your group. You may think that everything is going smoothly externally, but internally there is lack of communication.
I think the best way to become culturally understanding is to go to your subordinates and be completely open about race, ethnicity, religion, etc. Ask informed questions about their background and the comfort level will, in time, increase.