Jewish Festivals are listed in the Torah and are of two types: 

1. Three pilgrimage festivals (shalosh regalim):

• Passover,
• Shavuot, and
• Sukkot (including Shimini Atzeret).

These festivals were celebrated in ancient times by "appearing before God"--by bringing offerings to the Tabernacle or Temple.

2. High Holidays: 

• The Jewish New Year (Rosh Hashana—“Yom Teru'a” in the Torah), and the
• Day of Atonement (Yom Kippur).

 
Duration
Jewish holidays that were originally one day are now observed as follows:

• Rosh Hashana--2 days.
• Yom Kippur--1 day.
• Shavuot--1 day in Eretz Yisrael or 2 days elsewhere.
• Passover has festival days at the beginning and end of the holiday and intermediary days of lesser holiness, which are called chol ha'moed. In Eretz Yisrael, Passover lasts for 7 days in total and the first and last days are festival days. Outside of Eretz Yisrael, Passover lasts 8 days and has two festival days at the beginning and two at the end.
• Sukkot has festival days at the beginning and at the end and intermediary days of lesser holiness, which are called chol ha'moed. In Eretz Yisrael, Sukkot lasts for 8 days and the first and last days are festival days (the last day is Shimini Atzeret). Outside of Eretz Yisrael, Sukkot lasts for 9 days and the first two days and last days are festival days (the 8th day is Shimini Atzeret and the 9th day is Simchat Torah).

Character
Each holiday contributes its own character to Jewish life (Passover--the theme of freedom; Yom Kippur brings atonement, etc.). 

Celebrating
How to celebrate these holidays is detailed in our Oral Law and halacha books. Jewish festivals as practiced today are similar in holiness to Shabbat. As with Shabbat, the Jewish festival has candle lighting, kiddush at two meals, and havdala.   We eat our best food and wear our best clothing on Jewish festivals (we eat our next-best food and wear our next-best clothing on Shabbat!).
The main idea behind eating meals on Jewish festivals is joy (simcha), so you should drink wine and eat meat (only if you enjoy wine and meat).  There is no third meal on Jewish festivals since people used to eat two meals each day (adding a third meal on Shabbat was for enjoyment/oneg).
 
Melachot
Any activities or actions permitted on Shabbat are also permitted on the Jewish festivals. Actions that are forbidden on Shabbat are generally also forbidden on Jewish festivals, but there are some leniencies (only if the actions are needed for that festival day).
Examples

• Lighting from an existing flame,
• Cooking and baking for the Jewish festival day, and
• Carrying outside the eruv (hotza'a--transferring objects between domains).

 
Grama
Grama (indirectly causing an action) is permitted on Jewish festivals (but not on Shabbat). For example, you may advance or delay a timer that will make a light go on or off in the future (the timer must already be plugged in and operating from before sunset of the festival day).
Note For an action to be considered indirect based on time, there must be at least 2.5 seconds after the first action is done before the resulting action begins to happen.

Psik Reisha Dla Neicha Lei
Psik reisha dla neicha lei is forbidden on Jewish festivals, just as it is on Shabbat.

D'oraita Restrictions
D'oraita restrictions apply world-wide to:

• First and seventh days of Passover,
• First and eighth days of Sukkot,
• First day of Shavuot,
• Yom Kippur,
• First day of Rosh Hashana.

Note The same restrictions apply to all other Jewish festival days but are rabbinical.
 
Women
In general, women are not required to perform the positive, time-dependent commandments. Women and girls are not required to eat any Jewish festival meals except the Passover seder meal (but they are not allowed to fast on those days).

“Be holy because I, the Lord your God, am holy.” Leviticus/Vayikra 19:2
 
Halacha ("The Way To Go" or "Way to Walk") guides proper Jewish behavior in all aspects of life, each day of our lives--not just in civil laws or court situations. Halacha teaches us how to behave with our families, relatives, and strangers as well as how to fulfill our religious requirements between ourselves and God.

To fulfill our role as a holy people, we imitate God's actions. Examples are visiting the sick, welcoming guests, giving charity, refraining from creative activity on Shabbat, and promoting peace between husband and wife (shalom bayit).

The true reason for following halacha is because God commanded us to do so.  We observe halacha to please our Creator and to become spiritually close to Him by doing His will and imitating His actions.

Like the word for the whole body of Jewish "laws," each rule of how to act is called a halacha (plural, halachot).

Where Do Halachot Come From?

Although you will find halachot on this site that were born only a few days or a few decades ago, the body of halacha has been around since before creation.  "God looked into the Torah and created the world," says the Zohar, and so we find the Patriarchs followed halacha even before that great law book, the Torah, was given on Mount Sinai four centuries later.
 
Many halachot are specified in the Written Torah (Jewish Bible). These halachot correspond to fuller and more detailed halachot given orally (Oral Torah) to Moses on Mount Sinai to explain the Written Torah that he received at the same time. Many halachot could not be understood from the Written Torah without the Oral Law (for example, what should be written on a mezuza scroll?) and many common practices such as making kiddush or what tefilin should look like are to be found nowhere in the Written Torah.
 
Since the Torah applies to all generations, the Torah specifies that there be wise and learned people to decide how to apply halacha to the situations of the day.  Halachot can be found in sourcebooks such as the Mishna, Gemara, their commentaries, Shulchan Aruch, Mishna Berura, and responsa (questions and answers originally sent by letter and now, occasionally, by email or SMS!) of later rabbis.
 
Sometimes a custom becomes a halacha, sometimes not.  For example, the original halacha for tzitzit was that a Jewish man who wears a four-cornered garment must have tzitziyot on each corner.  The custom, which has become universally accepted and now has the force of halacha, is that Jewish men wear a four-cornered garment in order to be able to fulfill the commandment of wearing tzitziyot.  An example of a custom that did not become a halacha is that some men and boys wear their tzitziyot outside of their shirts and pants.

Levels of Halachot

In halacha, there are three levels of what to follow or observe. They are differentiated on this website by the following terms: 

• “Must”:  Halachot that are generally non-negotiable except in extreme situations;
• “Should”:  Customs that have been accepted by the entire Jewish world (or major segments of it) and that may be overridden when necessary, sometimes even if not extreme circumstances; and
• “Non-Binding Custom”:  Customs that are not universally followed and that do not need to be followed except by people who have the tradition to do so.

All of the Jewish festival holidays had an agricultural element to them.
 
Agricultural laws include Kilayim, Orla, Reishit, Teruma/Ma'aser, Shmita, and Yashan, as well as special laws applying only to fruit trees. Some of these laws still apply today by Torah law (d'oraita) while others, such as First Fruits (bikurim), only apply when the Jerusalem Temple stands and so are not practiced now. Others are observed today as "practice" for when the Temple is rebuilt.