Before we look at a Double Sedra, we should understand what a Sedra is.
Briefly, a Sedra is one of the sub-divisions of the Torah - the Five Books of Moses (Genesis, Exodus, Leviticus, Numbers and Deuteronomy). These five books are then split into Sidrot (the plural), totalling 54.
One Sedra is read every week in the Synagogue. And the whole lot is read every year. Starting to see a problem?
The Jewish year is based on a lunar calendar, and has 354 days in a "normal" year and 383 in a leap year (leap years occur 7 times every 19 years). This means that in a normal year there are 50.5 weeks and in a leap year there are 54.5 weeks.
But it's not that simple. The very last Sedra (V'Zot Habrachah) is always read on Simchat Torah so that comes out of the 54 we need to fit in. On the other hand, if any other Festival falls on Shabbat, we read the festival reading and not the normal weekly reading. The bare minimum number this affects is 2, but can be 5 or 6.
So, we have 53 Sidrot to fit in, with a maximum of 53 weeks (a leap year where the first day of the year is a Thursday will have a Shabbat as day 3 and also right at the end, less the minimum of 2 weeks that are taken up for festivals). This means that very occasionally (with the Jewish year 5765 - 2004/2005 being a case) there is no need for a double Sedra at all).
In most other years, on at least one occasion (and often more), two Sidrot are read straight through on one Shabbat. There are a number of standard Sidrot that are doubled up, and which ones are used in a particular year depends on various other things. But they are standardised around the world (although see note below about Israel).
- Achrei Mot-Kedoshim
- Matot-Masei (the longest double sedra possible).
- Nitzavim-Vayeilech (at a total of 70 verses, shorter than most single sidrot)
In Israel, things can get slightly different. Most Festivals are celebrated one day shorter in Israel (see Second day Yom Tov). Sometimes, the last day in Israel would be a Friday, and the last day of the festival outside of Israel would be a Shabbat. This means that on the Shabbat, Israel is reading the next "regular reading", and the rest of the world is reading the Festival reading. The following week, Israel reads the next one, and the rest of the world reads the one Israel read on the last day of the Festival. This means the reading can be out of sync between Israel and the rest of the world. This is then fixed by having an extra double sedra in the rest of the world when it comes round.