College Pro vice-president Leighton T. Healey explains that he can learn a lot from the candidate based on their reaction to this question.

Starting with your first memory, take 10ÔÇô15 minutes and tell me your life story. Please include all the ups and downs, pivotal and formative experiences, and how your family plays into your story.
This question requires a candidate do a lot of work and reveal to me, the interviewer, a plethora of personal information. For starters, most candidates will never anticipate a question like this and I'm able to learn a great deal from their reaction to the question. A guarded response tells as much as a gushing fountain. Specifically, when this question is supported by probing questions with genuine curiosity, an interviewer can get a pulse on whether a candidate externalizes blame, takes ownership of setbacks, craves community, dislikes authority, works well with teams, and had a quality nurturing experience.
This question helps me gauge how introspective the candidate is, meaning how apt they are at reflecting on their role in the world around them, a key indicator of receptiveness to feedback and input from a supervisor. It also allows an interviewer to gauge the candidate's self-confidence, ability to overcome obstacles, and whether they truly are the sum of the magnificent words they used on their resum├®.
An interviewer knows their company's culture, its needs and priorities. Through active listening and getting a full sense of the candidate as a person, questions like this allow an interviewer to weigh a wealth of real information against what they know of their organization and ultimately make a decision of whether this person would be able to align with the trajectory and groove with the resonance of the organization.
An appropriate way to respond to this question is to respond honestly and fully. An interviewer asking this question is not looking for a perfect nuclear family, high school valedictorian response. The interviewer wants to get to know you'the real you. It's not about getting a job; it's about succeeding in a career. Trust the interviewer, show your true human colours, dive into your passions, share some real obstacles you've had to face, and let the interviewer do their job.
If you take this advice, I can't guarantee that you'll get the job but I will guarantee that you will be a memorable candidate in a sea of applicants, and standing out is a great first step.