When I taught employment interviewing, there was one interview question that I felt was so common and so important that I made every student give a 1-minute presentation in front of the class answering it. That question is "Tell me about yourself."
A good interviewer will open with a question like this for a number of reasons: It reminds them which candidate you are (in the midst of multiple interviews), it lets them know which aspects of your background you think are most important or relevant, and it gives them an immediate snapshot of your communication skills by making you answer an extremely broad question as concisely as possible.
This is not the opportunity to talk about your personal life. Where you were born, details about your family, and information about your hobbies have no place in answering this question unless you are 100% sure they're relevant and you can tie them directly to the job at hand in one sentence (for example, saying that you're willing to leave a current job to move closer to family in the local area).
This is also not a chance to regurgitate your resume. They've read your resume; they know which college you went to, which degree you got, and where you're working now. Simply listing off those facts isn't helpful. This is your opportunity to tie together the pieces of your background into a coherent story.
What you talk about will be unique to you, but if you're having trouble figuring out where to start, try this acronym: EASE. It stands for Education, Activities, Skills, and Experience. (If you're out of college and have a few years' experience under your belt, I suggest replacing the Activities section with additional talk about Experience.)
Here's what this looks like in practice:
I'm a senior at the University of Washington, where I plan to complete a degree in psychology this coming spring. During my time at UW I've been involved in a number of different groups, including German Club, Circle K, and student government. In all of these groups, I started volunteering to create advertising for upcoming events, and I found I really enjoyed applying what I had learned about how people think to encourage people to attend events. I took several classes to improve my design skills, which I then further developed through an internship with XYZ Firm last summer. That experience taught me a lot about the business side of the house, and I feel that it prepared me well to take on this new role at your company.
You can see how this weaves a number of different aspects of one's background — psychology, design, advertising, business — into a single narrative. And that narrative should always lead to a simple conclusion: That is why I've applied for this job.