Benedict's abdication comes a surprise to most, even within the Vatican
Pope Benedict XVI has announced that he will abdicate the papacy, effective February 28th at 20:00. He cited health reasons for his decision: "After having repeatedly examined my conscience before God, I have come to the certainty that my strengths, due to an advanced age, are no longer suited to an adequate exercise of the Petrine ministry." (Read the full text of his announcement; watch a video of his announcement with an English translation.)
On the day of the announcement, Benedict tweeted: "We must trust in the mighty power of God’s mercy. We are all sinners, but His grace transforms us and makes us new."
“The pope took us by surprise,” said Father Lombardi [the Vatican spokesperson], who explained that many cardinals were in Rome on Monday for a ceremony at the Vatican and heard the pope’s address. Italy’s prime minister, Mario Monti, said he was “very shaken by the unexpected news.”
Pope Benedict XVI is at least the fifth pope in history abdicate. The other four popes abdicated due to scandal or grave problems in the Church; this is the first time a pope has abdicated due to ill health or old age under otherwise positive circumstances. (Read about the other four popes that abdicated.)
Following his abdication of the papacy at the end of the month, a conclave of Cardinals will be convoked to elect a new bishop of Rome, or Pope. See Aleteia's article explaining this process. Vatican Insider also has an interactive graphic explaining the process. RomeReports answers the question, Who's in charge when a Pope leaves his post?
Once he has abdicated the papcy, Benedict will remain a bishop but will no longer have any powers of the papacy, e.g. infallibility.
Rome Reports has a short biography of Pope Benedict XVI.
Pope Benedict XVI was the 265th Pope; see a list of all the Church's Pope over the last 2000 years.