This is an interesting question; the essay could be intended for a cultural-studies class, or for an application for a position abroad. It could be written in a number of ways.
For example, if you are intending to visit Korea in order to visit family or trace your heritage, you would use personal anecdotes and mention sites and families that are important to you. The use of personal information makes the essay more intimate and more honest than using external information.
Another possibility is applying for a working position in Korea. In this case, you should focus on your skills and strengths, explaining why you are the best person to travel abroad and work in Korea. Your desire to help, to teach, or to provide a unique skill-set are all potential topics. You should focus on yourself, not on preconceived notions or external information.
For a class, the essay should be more formal; focus on the qualities of Korea that you wish to experience, whether it be the culture, religion, or environment. Enriching your own experiences by visiting historical sites is a good way to research and learn about the history and culture, and this can extend into your wish to experience them personally instead of simply reading about them.
Finally, make sure you present a clear, simple, and honest thesis statement: "I want to visit Korea because I want to research my cultural heritage" scans better than "I want to visit Korea so I can take pictures for my blog." You can find much more information on essay format at the OWL at Purdue.