A cultural conflict is a conflict that comes from a particular cultural identity or perspective. This can be internal or external. For example, an external one would occur if you have a conflict with someone from another culture. An internal one would be one in which you doubt your own cultural values.
This type of conflict can help you clarify how your cultural identity influences your perspective. For example, by discussing your views with another person you might clarify what your cultural values are. Moreover, if the conflict is with yourself, you might be able to reassess how important a particular cultural value is in your life.