Eiruv Tavshilin
It is forbidden on a holiday to do any act in preparation for the following day. The one exception is when the holiday is followed by Shabbat, in which case, cooking is permissible on Friday through a mechanism known as an eruv tavshilin, whereby the cooking process is begun prior to the holiday.
If a holiday day -- whether the first or second day of a holiday -- falls on a Friday, an eruv tavshilin is set aside on the day preceding the holiday (Wednesday or Thursday afternoon), so that we will be permitted to prepare for Shabbat (cooking as well as any other necessary preparations) on the holiday. Only one eruv is required per household.
This eruv consists of a challah or two matzahs, and a cooked food, such as meat, fish, or an unpeeled hard-boiled egg.
Take the food items (it is a good idea to wrap them in aluminum foil, or another distinctive packaging, to easily keep them apart from the rest of the foods in your home), and give them to another person (if possible an individual who is a non-dependant), and say:
I hereby grant a share in this eruv to anyone who wishes to participate in it and to depend on it.
The one holding the food raises it a handbreadth, and then returns it to the person making the eruv, who then recites the following:
Blessed are you, L-rd our G‑d, king of the universe, who has sanctified us with his commandments, and commanded us concerning the mitzvah of eruv.
Through this [eruv] it shall be permissible for us to bake, cook, put away a dish [to preserve its heat], kindle a light, prepare, and do on the holiday all that is necessary for Shabbat -- for us and for all the Israelites who dwell in this city.
The eruv is put away until Shabbat, when it is eaten. In many communities, it is customary to use the challah or matzah as one of the two loaves of bread used at the Shabbat meal.
Important notes:
The eruv tavshilin only allows food preparations if the food will be ready with ample time remaining before Shabbat; enough time to theoretically allow the food to be consumed before sunset (if a troop of guests happens to trudge in to your home). This is an importnat detail to bear in mind when preparing the cholent, which cooks on the stove until the following day.
The eruv tavshilin only allows one to cook on Friday for Shabbat, it does not permit cooking from one day of the holiday to the next (i.e. Thursday for Friday).
On holidays it is only permissible to cook from a pre-existent flame, one that is burning since the onset of the holiday.
More on Eiruv Tavshilin
According to biblical law, it is permitted to prepare on a holiday day for a Shabbat that immediately follows, provided that the preparations are concluded leaving ample time before Shabbat enters—enough time to allow for the prepared food to be eaten before Friday's sunset.
Nevertheless, the sages prohibited food preparation on a yom tov (holiday) Friday day for the sake of Shabbat, unless an eruv tavshilin is set aside before the onset of the holiday. An eruv tavshilin consists of a cooked food (minimum one ounce) and bread or matzah (minimum two ounces, and preferably a complete loaf or matzah). These two food items are prepared and set aside for Shabbat before the holiday, symbolically serving as the beginning of the preparation of food for Shabbat. Thus, any subsequent cooking done on yom tov is considered to be a continuation and completion of the preparation begun beforehand.
There are two reasons for this rabbinic institution:
a) Concern for the honor of yom tov: This injunction impresses on people the importance of yom tov. After all, it is forbidden to prepare on yom tov even for the sake of the holy Shabbat. How much more so is it forbidden to prepare on yom tov for a following weekday!
b) Concern for the honor of Shabbat: When Shabbat follows yom tov, there is the concern that one's attention will be focused on yom tov, which arrives first, and pay less attention to the Shabbat that follows. The eruv tavshilin compels the person to begin preparation for Shabbat even before yom tov begins, thus reminding him to reserve choice dishes for Shabbat, too.
What if I forgot to set aside an eruv tavshilin?
Strictly speaking, if one forgot to set aside an eruv tavshilin, he is not permitted to prepare anything on yom tov for Shabbat. Luckily, however, there is some leeway.
When a person sets aside his own eruv tavshilin, he is allowed to stipulate that this eruv is also on behalf of all the Jews who live in the vicinity, so that they too will be permitted to cook on yom tov for use on Shabbat—even if they did not set aside their own eruv tavshilin.
And in fact, it is common practice for the rabbi of every community to do just that—to include all the Jewish members of the neighborhood in his personal eruv.
This, however, does not absolve the city's inhabitants from making their own eruvs. This is a loophole to be employed only by individuals who due to their preoccupation on the day before yom tov had forgotten to make their own eruv—not for people who were negligent or purposely did not set aside their own.
If one forgot to set aside an eruv before a two-day holiday that falls on Thursday and Friday, an eruv can still be set aside on Thursday—though the procedure is different. Consult with your rabbi if you find yourself in this situation.
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