When a stranger asks you that question, what do you respond with?
Do you simply tell them your name, your age, and your profession?
If someone truly wants to know who you are, I'm sure they're looking for more than that.
Answering this question in detail really makes you consider your current life and the person you have become.
What are your most fascinating skills, attributes, successes, etc.? Is that what makes you who you are?