A Siyum, which means completion, means the completion of any unit of Torah study, or book of the Mishnah or Talmud in Judaism. A siyum is usually followed by a celebratory meal, or seudat mitzvah, a meal in honor of a mitzvah, or commandment. Siyum also refers to the celebration.
An enduring custom is for the community to complete a unit of Torah or tractate(s) of Talmud during the 30 days following the death of a beloved one and hold a communal siyum thereafter, in tribute and honor of the memory of the deceased.
It has become customary for synagogues to arrange a siyum on the morning before Pesach to allow those fasting for Ta’anit Bechorim (Fast of the Firstborn) to break their fast, taking advantage of the halakhic principle that prioritizes Torah study.
You are actually allowed to eat meat during a Siyum in the 9 days before Tisha B'Av, even though on normal circumstances, it is forbidden to eat meat during that time period.
A siyum ha-sefer, meaning “completion of the book,” is also held as a ceremonial completion and dedication of a sefer Torah, a handwritten copy of the Torah, the most important Jewish ritual object, which is kept in the Ark of a synagogue.
Usually, when an individual or a group conclude the study of any tractate of the Talmud, or even of the Mishnah, a siyum is celebrated. At the end of every volume of the Talmud a special hadran prayer is printed with a set order of prayers and a special kaddish, Kaddish D'itchadita, in honor of the completion of that volume, which Judaism considers to be an important achievement and a milestone worth celebrating.
In the merit and honor of a deceased individual, it is customary to undertake Mishnah study with the goal of holding a siyum.
Rabbi Moshe Feinstein, based on the Nemukei Yosef, the Ran (Rabbeinu Nissim), the Rashbam, and the Eliyah Rabbah, extends the concept of a siyum to include even a festive meal celebrating the completion of any mitzvah (commandment) that has taken a significant duration of time (such as a number of weeks or months).