If there's ever been a list of those things that sound especially Chinese, the character 孝(xiào) has to be one of them. Terms that go deep into Chinese culture often appear to be impossible to translate into western languages due to the huge difference between these languages and Chinese in nature. Western culture and Asian culture are completely different, especially for East and Southeast Asian nations. We have different value systems, social moral standards to judge a person and hold onto different philosophies and beliefs towards life. All these differences make 孝 so extremely important and special in Chinese culture, or more accurately, the culture in the whole East Asia. And this is why you can't perfectly translate this into English although you do have a phrase called "filial piety", which is not exactly the same as 孝 essentially.
As seen from the character itself, the bottom part is 子(zǐ), which means child, and the top represents the character 老(lǎo), which refers to elderly in the family. So the structure of the character vividly conveys the idea of 孝: the senior members of a family being supported and looked after by the younger generations.
Chinese culture is mainly influenced by two philosophies: Taoism and Confucianism. In Taoism, people are told to pursue a state called 无为(wú wéi) which literally means "doing nothing". But you may wonder how is it related to 孝? Well, to achieve 无为, Taoists believe that one must follow the rules of nature and accomplish oneself both physically and spiritually, in order to get rid of any "impurities" inside a person's body and mind. Taoism claims that a man can only live once, so one must be well educated, live healthily, enrich the mind regularly and substantially, follow moral values strictly and control human desires in order to sublime oneself. And here the idea of obeying moral values is introduced into the philosophy, and "filial piety" is undoubtedly one of the most essential human virtues.
When Confucianism came to the historical stage and gradually became the belief of the mainstream of the whole society, the concept of 君子(jūn zǐ) was regarded as a lifelong goal for a civil man. 君子 basically means an accomplished and well-educated man who is ideally thought to have no moral weakness. Based on that, in ancient times people tended to judge a person according to his moral values completely, and one's knowledge and talents were sometimes neglected. From then on, the Chinese culture had derived a series of virtues that determine a 君子. And 孝 was included as one of the main virtues. In Confucianism, there're five things regarded as the most worth worshipping, which are 天(tiān), 地(dì), 君(jūn), 亲(qīn), 师(shī), referring to the sky, the earth, the monarch, parents and teachers. You can see how much emphasis was being put onto 孝 just by the way Confucianism kind of equates the worship and respect of parents to that of the sky and the earth, given that the worship towards the nature was extremely strong in ancient times. There's also 百善孝为先(bǎi shàn xiào wéi xiān), "among all the virtues, 孝 comes first". During long history of China's ancient dynasties, 不孝 was continuously one of the most serious crime and listed as one of the ten most evil sins.
In ancient China, behaviours considered as 不孝罪(bù xiào zuì, crime of 不孝) include:
-report or reveal your parents' crimes
-say vulgarities to your parents
-curse your parents
-save money for yourself or move out of the family while your parents are living
-fail to try your best to support and satisfy your parents in their lives
-get married during your parents' funeral period
-have entertainment activities during your parents' funeral period
-take off funeral clothing and wear colourful clothes during your parents' funeral period
-conceal your parents' death, don't tell others about their death or don't arrange a funeral
-lie that your parents have died
孝 helps construct a society in China in which people instinctively take up their duties to look after the parents, giving them full respect and supporting them both financially and mentally with the best efforts. And it's also seen as a person's very responsibility to obey the parents without any condition and a despicable behaviour to talk back to the parents to defy them in an aggressive manner. There's a saying, 小杖受大杖走(xiǎo zhàng shòu dà zhàng zǒu), meaning that when your parents punish you mildly, you have to be willing to receive it, but you should hide from those fierce punishments. Though here it mentions you needn't accept your parents' criticism all the time, the best you can do is only to run away rather than "fight back". Therefore according to 孝, you're not supposed to go against your parents under any situation even though they're unreasonable or wrong.
The concept of 孝 also strengthens an unshakeable respect and tolerance towards the elderly. In Tang Dynasty, an elderly person (maybe over 80 or so I'm not sure about the age) could practically shit on the floor of the emperor's palace without being punished at all because that was his right based on the age. One of the most well-known dictum of Confucius is 七十而从心所欲，不逾矩, meaning that after 70 years old, one can do whatever he wants and anything he does is seen as acceptable. This spirit in Chinese culture establishes great protection, respect, understanding and support for elderly population, making the society more harmonious and stable.
However it also led to problems. The most infamous one is the excessively extreme emphasis on 孝. To promote the virtue of 孝, some scholars in ancient times invented a series of stories called 二十四孝(èr shí sì xiào), The 24 Stories of 孝, some of which are ridiculous and against human nature in a modern view. One of the stories describes a man killed his own son who was only a baby just to ensure his mother could eat enough food during the famine, which is totally inhuman. In history till now, Chinese people have been continuously making efforts to cut off these negative aspects in 孝. Traditionally, we have a Chengyu, 大义灭亲(dà yì miè qīn), which means to sacrifice the relationship between families for the sake of justice, usually involving reporting your relatives' crimes. In modern times, while the government is still trying hard to protect the traditional 孝 spirit, they also encourage people to objectively and properly view it. There're official legislation and law made to regulate inappropriate behaviour and crimes related to 孝 which are much more reasonable than the ancient ones. Also, the government collaborated with several organisations to come out The New 24 Stories of 孝 and they're closer to our real life and more relevant to the present era.
The world is changing, so is the concept of 孝. However, no matter how it adapts to the current society, one thing will remain unchanged and that's the care, support and respect towards the parents and 孝 will definitely be kept as one of the core ideologies of Chinese culture forever.