As the term suggests, cross-cultural training promotes communicating or interacting with someone from another culture. Our national cultures are learned in childhood, mostly unconsciously, so we take our own ways of doing things for granted. It's only when we bump up against people who do things differently that we become aware of our own habits. And it's the unexpectedness of culturally different behaviors that makes them seem rude or uncivilized and can lead to negative perceptions. When our own ways are challenged or questioned, it's easy to misinterpret unfamiliar behaviors and responses as intentional mistreatment.
Politeness is a good example.
All cultures have ways of being polite, but not all situations call for polite behavior in all cultures. For example, Americans are taught to be polite to strangers in public. So an American in Hong Kong might perceive a shopkeeper or postal clerk as being unfriendly, abrupt or rude, when in fact they are just treating you like any other customer. It's also important to remember that some behaviors that carry a positive meaning in one culture are negative or have no significance in another. Silence or no response can be very frustrating if you don't know how to interpret it in a given cultural context.