This quote means that the speaker wants to use dialogue, or talking, and culture, or the ways of life, customs, and values of different people, as a way to bring people from different cultures together. Doing this could help solve conflicts between different groups of people. For example, if two groups have different beliefs or values, having members of each group talk to each other about those differences and learn more about each other’s culture could help the two groups find common ground and come to an agreement that works for both of them.