=What is Go?=
Go, also known as weiqi (in Chinese) or baduk (in Korean), is an ancient board game with a simple, abstract set of rules, but incredibly deep strategy.
More general info about the game and its history can be found at its wikipedia page:
http://en.wikipedia.org/wiki/Go_game
=Why play Go?=
Go is in the same broad family of abstract strategy games that contains chess, and offers similar (if not arguably more) strategic complexity. If you love chess for its strategic and tactical depth, then you'll mostly likely also fall in love with the game of go.
Despite the highly abstract and simple rules (where the game mechanics can be roughly summarized as: adjacent stones are connected, and surrounded stones are captured), profoundly deep strategy and tactics elegantly emerge from the objective of encircling the most territory and enemy stones. The game is about balancing the tactical urgency of local battles with the strategic aims of the whole-board war.
Go is perhaps the epitome of the cliche "moments to learn, but a lifetime to master", and you'll always be able to find joy in understanding new knowledge and uncovering its secrets.
=What is this Learn Go Week about?=
Learn Go Week is a broader effort in the go playing community to reach out to new/beginner players. OGS (online-go.com) is a web-based go server that is offering a program of lectures, teaching games, and tournaments for beginners of various levels (from complete novices to beginners with some experience that are looking to improve their game).
If you ever wanted to be introduced to the game or are a beginner that is feeling about lost about how to play, this would be a great opportunity to learn.