I'll explain in 3 parts: Chinese characters, spoken language or dialect, and written language.
Let's start with the Chinese characters, or Kanji, a word borrowed from Japanese. Chinese is a tonal language, not a phonetic one like English. Technically speaking, it doesn't employ an alphabet like "a", "b", "c", "d". Instead, each character denotes a concept.
There are around 10,000-20,000 everyday used characters nowadays. The number of characters has been increasing throughout history. The first Chinese dictionary, Shuowen Jiezi, published around the 2nd century, recorded around 10,000 characters. In the Qing dynasty, the Kangxi Dictionary, published in the early 18th century, recorded about 50,000 characters. Currently, it is estimated that there're a total of 80,000-90,000 characters. Characters are looked up via radical, or the root element of a character. This classification of characters by radicals was pioneered by Shuowen Jiezi, and is still being used widely today.
Around 200 BCE, the first emperor of China, Qin Shihuang, of Qin dynasty, re-instituted the standardization of Chinese characters, after he unified China. Thanks to this standardization, all Chinese can communicate with each other via the same written language, even though the spoken language varies from place to place.
It is important to point out that even with the standardization, other scripts existed throughout the history of China. Their birth and evolution were closely related to Chinese calligraphy. In our times, we have another example, simplified Chinese versus traditional Chinese, where the scripts differ. Mainland China uses simplified Chinese characters, whereas in Hong Kong and Taiwan, traditional Chinese characters are being used. From my conversation with mainland Chinese, they learned both traditional and simplified characters in school, but of course they use mainly the latter.
Secondly, the spoken language, or dialect rather.
Different parts of China speak different dialects. It's a common misunderstanding that Mandarin is the dialect spoken by people in Beijing. It is not. Beijing has its own dialect, even though it's very close to Mandarin. Since I was born in Hong Kong, my native tongue is Cantonese. It is another common misunderstanding that all people in the Guangdong province speak Cantonese. In fact, Cantonese is just one of the many dialects throughout the province. Taishan, about 100 miles west of Hong Kong, has its own distinct dialect. Chaozhou, about 200 miles north east of Hong Kong, speaks yet a completely different dialect. Cantonese refers to the dialect spoken in the city of Guangzhou. In general, the farther away from the city, the higher the chance that people speak something different than Cantonese. Hong Kong people speak Cantonese because (a) it's close to the city of Guangzhou (less than 100 miles), and (b) historically, most of its immigrants were either from Guangzhou or its vicinity.
So, what is Mandarin? Before we answer that question, we have to go back to Chinese history. China has always been a large country. Officials who worked for the central government came from places all over the country, thus all spoke a different dialect. To facilitate communication and administration, a dialect spoken among government officials was born. This dialect varies from dynasty to dynasty throughout the history of China. Today's Mandarin is derived from the "official" dialect of the previous dynasty, Qing dynasty. Because its capital was also in Beijing, Mandarin was therefore heavily influenced by that dialect. Also, because the imperial court of Qing dynasty was Manchurians, Mandarin was heavily influenced by the native dialects of the Manchurians as well.
Due to the government's effort around the turn of the last century, along with the push for standardized education, every Chinese knows how to speak Mandarin. That's why when a person travels from Shanghai to Xian, he/she can go into a restaurant and orders food via Mandarin. But after the waiter takes the order, it's likely that he/she will speak Xianese to the chef! By the same token, if a foreigner knows Mandarin, he/she should have no problem communicating with people throughout China. Theoretically, nobody's native tongue is Mandarin, since it's "man made" (see previous paragraph). A Chinese kid first speaks the native language of his/her own town or village, and he/she only learns Mandarin in school, albeit at a very small age.
Lastly, let's talk briefly about written Chinese.
There are, in general, two forms of written Chinese, classical Chinese and written form of spoken Chinese (baihua). Regarding classical Chinese, since that's a complicated topic by itself, I'll just say that it's not based on spoken Chinese and leave it like that. There is a learning curve (in fact, quite a steep one), even for Chinese, to read and write classical Chinese. The written form of spoken Chinese, or baihua, again, without getting into the details, is based on Mandarin. For instance, the famous Dream of the Red Chambers was written in baihua. All published materials today are in baihua.
When I was educated in Hong Kong during the 70s and 80s, students didn't learn Mandarin. But since the written form of spoken Chinese is based on Mandarin, how could I, who didn't know any Mandarin, possibly read any books then? I got this question a lot from foreigners. The answer goes back to our unified script. Because the meaning of the characters are the same, and most expressions are common whether it's in Mandarin or Cantonese, I was able to understand what I read. I was only able to pronounce the words in Cantonese but not Mandarin. Of course, if you get into the details, there're some Mandarin specific expressions but that doesn't change the big picture. Furthermore, when I am learning Mandarin, it's mostly just the pronunciation that I need to pay attention to. Everything else is just "Chinese"!
To summarize,
(a) Chinese characters are unified. They carry the same meaning. Expressions are common in almost all dialects.
(b) There are a lot of different dialects spoken throughout China. In other words, the spoken and the written forms of the Chinese language are related but separate.
(c) Mandarin is the standard, or official, spoken language. It was derived from the Beijing dialect for historical reasons. They're not the same dialect technically.
(d) Modern written Chinese is based on the spoken language of Mandarin. A person doesn't need to speak Mandarin in order to understand written Chinese (he does need to speak a Chinese dialect though). It is because Chinese characters and expressions transcends over all spoken Chinese languages.
(b) There are a lot of different dialects spoken throughout China. In other words, the spoken and the written forms of the Chinese language are related but separate.
(c) Mandarin is the standard, or official, spoken language. It was derived from the Beijing dialect for historical reasons. They're not the same dialect technically.
(d) Modern written Chinese is based on the spoken language of Mandarin. A person doesn't need to speak Mandarin in order to understand written Chinese (he does need to speak a Chinese dialect though). It is because Chinese characters and expressions transcends over all spoken Chinese languages.
