You want to show the interviewer that you think about brand experience and the promise of a brand. Showing that you understand suggests that you will keep their brand or their client's brand promise/experience front and center with your design choices.

Choose a brand that you have personally experienced and can articulate. Make sure you include the brand promise and how it affects the brand value. Translate your brand experience back to the work they are doing if possible.

The first brand that comes to mind for me is Apple. As a consumer of Apple products myself, I find their brand experience is outstanding. Apple products are expensive, but you get what you pay for - they work incredibly well, they're simple and they make everything easier. For example, if you buy an iPhone, it comes in packaging that feels well made and well designed. Everything is slick and the unboxing is intuitive and easy. The same can be said for the phone itself - it is well-made, has an intuitive interface and it is simple to use. That speaks to the brand promise. You know that by choosing Apple you are paying for a well-designed high quality device that is simple and intuitive to use.