Shovavim (Hebrew: שובבי"ם ) is an acrostic for the Jewish parshioth of "Shemot", "Va'era", "Bo", "B'Shallach", "Yitro" and "Mishpatim". The period in which those portions are read typically falls around January-February. Shovavim is a season in the Jewish calendar when the Kabbalists teach that it is auspicious to repent of sins, especially for sexually-related transgressions.
During this 6 week time period in the Hebrew calendar, it is customary to be more careful not to violate any of the sexually-related transgressions commanded in the Torah. Some have the customs of studying laws relating to such transgressions, fasting and giving extra tzedakah during this time, and of reciting Selichos and other Kabbalistic prayers and tikkunim (Kabbalistic prayers or meditations) designed to counteract their harmful effects.
There are those Jews who have a custom to fast every Monday and Thursday during these weeks. Some fast on Erev Shabbat until the afternoon.
The origin to these customs is based on Jewish Kabbalistic teachings and therefore Sephardic and Hassidic Jews are more likely to follow these customs than their Ashkenazic counterparts.
There are extra prayers added called "Tikkun Shovavim" during these weeks.
During a Jewish leap-year one sees references to an eight-week period called "Shovavim Tat", derived by adding the next two portions, "Terumah" and "Tetzaveh", to the list.