- "He who destroys a good book kills reason itself."
– John Milton
One of the cornerstones of civilization, Writing is the ability to transfer information to durable materials (stone, paper), and thus preserve it for the generations. It allows the beginning of the scientific development of your empire, by the construction of the Library, the first science building in the game.
This is an excellent technology for scientific civs such as China and Babylon to beeline, especially considering that the latter's unique ability provides a free Great Scientist. As Population is the main source of Science, a 50% bonus is quite hefty, and progression towards the National College can extend that bonus further.
Writing is the art of recording information on material (paper, stone, clay, animal skins) so that others who look at the material can discern its meaning. Invented sometime around the fourth millennium BC, the earliest form of writing was "pictography," in which the writer draws little pictures representing the subject matter. This may work adequately for very simple subjects, but other methods become necessary when more esoteric topics are discussed. (Drawing a picture of a sheep may be easy, but how about a picture of a thousand sheep, or a picture of the sound a sheep makes when it falls off of a pyramid? Not so easy.)
Logography probably came after pictography. In logography, symbols stand for individual words. There's a symbol for sheep, and another symbol for a thousand sheep, and yet another symbol for the sound a sheep makes when falling off of a pyramid. However, a full language may have tens of thousands of words in it, and learning the symbol for each word may be problematic.
A phonographic system provides a unique symbol for each different-sounding word. "Sheep" would have a unique symbol, but "there," "their," and "they're" would all share the same symbol. This results in a smaller number of symbols to memorize, but also in greater chances of misunderstanding.
In an alphabetic system, the language provides a set of symbols (the alphabet) which represent the various sounds which may occur in a language. These symbols can be strung together to replicate any spoken word in the language. Theoretically, anybody who can spell should be able to accurately "sound out" any written word. This is the system used in the English language, and is generally believed (especially by English-speakers) to be the most useful and flexible writing system yet devised.