The answer to this question probably depends a lot on whether the "cultural representative" aspect is a primary goal of the fellowship (e.g., if it is designed to enable artists and poets to travel), or if it is a secondary goal (e.g., they want to make sure contact between cultures is a byproduct of what you do).
If it's a primary goal, we probably can't help, and it's probably not for you unless your field is the arts (which I don't think it is).
If it's secondary, however, the big thing is probably to bring your head outside of work and talk about what you'd want to do with your outside time, interacting with the culture around you. For example, I recently hosted a visiting graduate student through Cultural Vistas "Train USA" program. One of the requirements for setting this up was to provide our plan for exposure to American culture, so I talked about some of the local events and places that I wanted to introduce our visitor to outside of work. And that's just what we did: my visitor was a good, social person, and enjoyed exploring the area, and though the specific selection of events and places ended up being a bit different than the examples I listed, the spirit was the same.
If the program that you are applying to is similar, then I would suggest it may be good to take a similar approach. Begin with the plan and assumption that you will be socializing with people outside of your work, and then talk about how others will get exposed to your background and experience through what you would like to do. Food is a nice example, if that's a thing you enjoy. Some others: do you play music, or enjoy poetry? Are there festivals and holidays whose celebration you would want to share? Are you a movie buff, and want to share locally made good or bad cinema? The list of possibilities is endless, and depends mostly on what it is that makes you a well-rounded person beyond your research.
Likewise, for the return home think about what people you know at home are likely to ask, and how you will share it with them. Are you a photographer? Do you blog? Are there local elementary schools you volunteer at where the kids would like to hear about traveling? Will the networking connections you build abroad help others to make similar journeys?
In short: think outside the research box, about the rest of what makes you a good and interesting human being.
