A representative office is kind of like having a pretend office in another country. Let's say your Mom works for a big company that sells toys. They want to sell more toys in another country called France, but they don't know much about the people and how they like to play with toys in France.
So, they decide to open a representative office in France. This office doesn't actually sell toys, but it helps the company learn more about the people and what they like. It's sort of like sending a friend to another country to learn about the people and bring back information.
The representative office might have people who speak the language and know the culture of France. They might go to toy stores and talk to people about what kind of toys they like. They might even have fun events to get people excited about the company's toys.
The big company can use the information they get from the representative office to make better toys that the people in France will really like. And when they sell more toys in France, they'll make more money too!