Find Your Niche: Identify and Focus

How do I find my niche market? How can I niche down in a socially innovative ideas? I agree that positioning is important, and one of the ways of doing it is to find my niche market. But how? 

Here is an article that I've found regarding finding a niche market:
http://www.entrepreneuronfire.com/focus-on-a-passion-to-find-your-niche/

It says, finding a niche market is a must if I want to start and grow a successful business, and I have to IDENTIFY my niche market and FOCUS on it. This post was written by Kate Erickson, content creator and community manager. When she tried to start her own business, at first, she made mistakes, by not focusing her clients. She had been liking writing, so wanted to target everyone who needed professional writing skills. But it did not work in that way. After spending a fair amount of time, waiting and wondering, she found out that people responded her when she said she can create "e-books". Then she started marketing herself as an e-book producer, using her writing skills still and focusing her clients in a narrower way.

Another article I found regarding niche also talks about being specific about the market. Here is the article:
http://www.iwillteachyoutoberich.com/blog/case-study-how-niching-down-helped-paige-nearly-double-her-number-of-clients/

This article is about a Pilates instructor, who used to work very hard but could not satisfy clients that much and did not have many clients as well. But later, when she started to focus her Pilates lessons for those who have back pains, her clients started to double, and the word of mouth about her class started to spread out very quickly.

This seems to be not very different: "I am a Pilates instructor" or "I’m a Pilates instructor working with clients with back injuries", but apparently, these a few more words made all the difference.

Likewise, if I were to become a personal trainer, I should be more specific like 2, rather than being focusing on everyone who could be interested in work-out like 1:

1. The trainer who promises everyone and anyone that working out will make them feel better
2. The trainer who promises 20-something men they’ll double the size of their biceps in four months

Then, what will be niche market? I am South Korean who have been exposed to many different cultures and societies. Having exposed to other countries, I realized that I am very strong in international environments -- I don't stressed out when I am surrounded with different people. I get energy by being unique, for example, I am the only Korean, only female, or only Asian. I like to learn and understand other cultures and be able to adept myself into them.

I feel like even at home when I am in Heinz or CMU. Heinz/CMU is made up of more than half of international students. I feel very comfortable in that. And my past experience has been also related to English literature, global business, international relations, and immigrants and refugees; therefore, I would be clearly comfortable and have fun by doing some work related to international environment but by being a unique Korean! Whether it can be an embassy work, liaisoning Koreans to non-Korean international people or introducing North Korean status to people out in the world, doing research and communicating with people from different countries, I would have fun with that.  

I hope to narrow down more of my niche market as this class goes along, but this is what I've found so far. And my question to everyone is: what do you think your niche market from your past personal experience and knowing where your passion and strength lies? Thanks!