Literally "Page of the Day".
This is used to refer to one of the Jewish methods of learning the Talmud. One (double-sided) page is studied every day, working through the entire Talmud. As there is a standardised format of the published Talmud, the same things are on the same page in every edition. Even editions which don't follow the normal pagination (eg the Steinsaltz edition) still mark up where the "traditional" pages start and end.
The entire process takes about 7 years and 5 months to read the 2711 pages. It was first instituted in 1923 by a Polish Rabbi to promote daily Jewish study, and today (2nd March 2005 / 21st Adar I 5765) represents the end of the 11th cycle, and the 12th cycle starts tomorrow and ends on 2nd August 2012 / 2nd Av 5771 (put it in your diaries). There is a general view in Judaism that you can never learn something too much - you can always find new explanations, or new messages, or use a new commentary, in the study. Talmud is no exception - there are commentaries, and commentaries on the commentaries, so each time you can learn something in new depth. It is also like on Simchat Torah, where we finish reading the Torah and immediately start it again. The Satan says to G-D "Look at the Jews, they'll never finish learning your book". Then he says "Look, they've finished it, but they'll never look at it again". And on starting again, he is truly vanquished.
The calendar is published worldwide, so everybody is learning the same page on the same day. Many synagogues have a Daf Yomi Shiur (study session) daily, so even if you are out of town, you can find other people learning exactly the same piece of text that you are.
At the end of learning any book of Talmud, it is traditional to have a small celebratory meal called a Siyum. At the end of a Daf Yomi cycle, because it represents learning the entire Talmud, there are large parties (even at Madison Square Garden) for people who have been involved to get together.