What is the weekly Torah portion?
The parashah (or Parashat HaShavua, “the portion of the week”) is the section of the Torah read publicly in the synagogue every Shabbat morning. Week after week, the Jewish people move through all Five Books in a single year.
54 portions, one cycle a year
The Torah is divided into 54 parashiot. Each takes its name from one of the first distinctive words of its text: Bereshit (“in the beginning”), Noach, Lech-Lecha, Vayera. Each Shabbat's parashah is read from a hand-written Sefer Torah and divided into seven aliyot, each one a call-up to the Torah.
The cycle begins right after Simchat Torah with Bereshit and ends the following Simchat Torah with Vezot Haberachah, when the last chapter of Devarim is completed and the first verse is immediately read again. The Torah has no end: when you finish, you begin again.
Why some weeks read two parashiot
The Jewish calendar is lunisolar, so the number of available Shabbatot changes from year to year. In regular years some short parashiot are read together, such as Behar-Bechukotai, Matot-Masei or Nitzavim-Vayeilech. In leap years, with an extra month of Adar, they are read separately.
When a festival falls on Shabbat, the festival's own reading replaces the parashah, which is postponed. Because the Diaspora keeps one more festival day than Israel, the two communities sometimes read different parashiot for a few weeks until they line up again.
Reading, studying, reviewing
According to the Talmud (Bava Kamma 82a), the public Torah reading on Mondays, Thursdays and Shabbat goes back to Moshe Rabbeinu, so that the people would never go three days without Torah, and Ezra extended it. On Mondays, Thursdays and Shabbat afternoon the opening of the next parashah is read.
Beyond listening, the tradition asks each person to review the parashah during the week: shnayim mikra ve'echad targum, the text twice and the translation once. The Shulchan Aruch (Orach Chayim 285:2) teaches that Rashi's commentary may take the place of the targum.