24 Tevet

The month of Tevet is the 10^th month of the year.  The number 10 as the Maharal says, is associated with a a שלימות.  What is the שלימות of Tevet?  There are no holidays this month, in fact, there is a fast day on the 10^th day of the month?

The point of the entire golus is for the geulah that comes forth from it.  Although, of course 10 Tevet, the day of the siege of Yerushaliyim is a fast day because of the terrible events that occurred, the light of the redemption was already planted in the start of the golus.  The cause of the golus was sinas chinum and in the siege was already the tikkun for everyone was forced to come together and support each other.  The possuk in Yechezkal (24:2) says סמך מלך בבל אל ירושלם בעצם היום הזה.  Why use the word סמך which indicates helping out and supporting?  Because in the very planting of the seeds of golus itself, the road to tikkun was already being paved.  That is why it is very fitting for the fast day to be on 10 of 10 because the fasting is to reach the teshuva that is demanded of the day which brings out the pnimious of the day, which is to lead to the geulah as will be appreciated when it will be turned to a day of שחמה וששון.

The Gemorah Megillah (13a) says that Tevet is the month שהגוף נהנה מן הגוף.  This is a reflection of the way things are in the spiritual realm as well.  Just as two separate bodies warm each other in the cold month of Tevet, so too the world in the month of Tevet is devoid of the open, warm rays of the presence of Hashem, and it is up to Klal Yisroel to bring a warmth to the world through their avodah.  The month of Tevet is the month of warming the guf.  This is also reflective of the ability to rise out of the golus.  Klal Yisroel is united at the neshema level, it is the separate bodies that lead to sinas chinum and the need for golus.  This month gives us the ability to become united at the גוף level as well. 

The yom hilulah of the alter Rebbe is 24 Tevet.  The Alter Rebbe sought to infuse the cold מוחין with the warmth of the light of chassidus.  That is why his yom hilulah is this month of Tevet.  The number 24 is the amount of letters of ברוך שם, which is the avodah of יחודא תתאה, to recognize Hashem's presence in this world.  This was one of the major chiddushim of the Besht and elucidated in the works of the Alter Rebbe that Hashem's presence can be felt and accessed in this world.  (Largely based upon Likutay Sichos volume 25 on 10 Tevet and volume 25 on Tevet.)