Chinese view offering cigarettes to strangers they are talking to as normal. It's a conversation lubricant between strangers. When you hang out with acquaintances, it is impolite if you start smoking without offering one to the others. It's all about cigarette etiquette.
China has its own unique cigarette culture. We barely see people serving cigarettes to each other in European countries or the US. They only share a cigarette when they want to ease the nerves on a battlefield and bond as the brothers. Serving cigarettes happens more often in China.
Serving a cigarette is good manners. When we meet our boss, we serve a cigarette to him to show our respect. When we talk to somebody, we offer a cigarette as a peace offering, which will build trust observably. We thank our plumber with his fee and a cigarette, We serve a cigarette to a guest, suggesting "You are very welcome." A cigarette (a nice cigarette is better) is an external, material expression of a compliment. To our shy, not-good-with-words Chinese, cigarettes helps us talk.
In many places in China, the cigarette brand could also represent one's social status. It is kind of a cigarette version of "You are what you smoke." China has many kinds of cigarettes and a huge price gap between different cigarette brands while cigarettes in other countries have similar prices, some are even the same.
Chunghwa, as a symbol of a high-end cigarette brand in China, has very high sales in China. It was on a short allowance until 1988. Anyone who carries a Chunghwa cigarette between his or her fingers is regarded as upper-class or a wealthy man or woman. Panda, another prestigious cigarette brand, is also scrambled by people who like smoking. People believe cigarettes establish one's social class. If you are holding a low-end cigarette, you are probably a nobody.