Federico Lombardi, who is the spokesman for the Vatican, announced that it will be between 15 and 19 March when performing they will hold a conclave to elect a new pope.
The ecclesiastical rules indicate that 15 to 20 days must first go by after a leader dies or resigns from the position, before holding a new election for a new Pope. Benedict XVI will discontinue his functions as the current Pope on February 28 at around 8p.m. (Vatican local time), in which then his seat will be "vacant." Soon after, the Cardinals will set the exact date for the election of the new Pope.
Benedict XVI, whose real name is actually Joseph Ratzinger, announced his resignation on February 11, 2013, saying he was too tired to continue in his post as the Pope, which the Vatican also recently confirmed that the Pope had a pacemaker.
Others have indicated that his resignation is due to the problems that the Catholic Church has faced during his tenure. Problems like sex abuse scandals, private documents coming to light and internal power struggles, and much more.