A phrase in British slang that denotes the process of making fun of someone (I'm given to believe that it refers especially to making someone with a large ego look foolish, though that is just a personal interpretation). This phrase is said to be derived from one documented in the late eighteenth century, "piss-proud", which today is used to describe someone who has an overinflated sense of his own importance. In the most basic sense, a false erection caused by a full bladder disappears once the owner of said erection urinates; thus, to "take the piss" from someone generally means to defuse their baseless arrogance through mockery or irony, although the phrase is often also used to describe someone's (the piss-taker's) refusal to take a matter seriously.
Example: British student Luke Thompson on Ali G, a character on a television show who is black, uneducated, and misogynistic, and who is played by a white, university-educated, Jewish man: "He's funny, the way he talks and that...He's just taking the piss out of the groups who go around thinking they're hard, starting fights and that."*
Though "piss-proud" as an expression was in use from the eighteenth century onwards, the phrase "taking the piss" and its permutations (such as "piss-take") did not surface until the twentieth century. As the word "piss" continued moving into the realm of vulgarity, the phrase spawned a euphemism: "taking the micturations", or "taking the mickey", which has in turn ended up with variations of its own such as "mike-take" and "extracting the Michael
", even though the original phrase had nothing to do with the name Michael.
Sources
BBC - h2g2 - The Origins and Common Usage of British Swear-words <http://www.bbc.co.uk/dna/h2g2/A753527>
*"Is it cos I is black?" Guardian Unlimited Special Report <http://www.guardian.co.uk/ali/article/0,2763,195449,00.html>
Online Slang Dictionary <http://www.ocf.berkeley.edu/~wrader/slang/t.html>
World Wide Worlds <http://www.quinion.com/words/qa/qa-tak2.htm>