Culture encompasses the shared patterns of knowledge and interest of social groups where they have common characteristics like language, religion, social norms, music, arts, dances, and pretty much anything that defines the local individuality. Every locality has its own culture, but with globalization, many cultures have spread to much larger areas or become famous tourist attractions for people all over the world.
Eastern culture, generally considers cultures of the far east including China, Japan, Vietnam, North Korea, South Korea, Taiwan, the Indian subcontinent, etc. As a broad generalization, Eastern cultures are a lot more conservative, and family oriented in the east. For example, Indians have an age-old custom to touch the feet of their elders when greeting them as a show of respect. Similarly, East Asians often have a culture of bowing in the place of greetings, apologies, and thanks. These are rigid ideologies that have been followed by generations in these areas and are something that defines who they are. This will probably continue to stay a social norm in these areas for many further generations as it is one of the defining factors of the area.
Western culture, usually referring to European and American states, talks about wild individualism. The west focuses on everyone defining themselves in a new way to leave their mark. That might be why family names become increasingly unimportant in the west. The culture teaches people to focus on themselves while loving the country. It is in itself another unique and interesting culture as well.
When you think about how these cultures came to play, there are many factors that you can think of. Of course, a lot of cultures originated from religious beliefs when religion was spreading through the lands. Some things came from ancestral practices and interests. Some cultures can be older than others but they are all very interesting to learn.