Spiritual Purpose of Chanukah

בספר קדושת לוי כי חנוכה התחלת הימים טובים בשנה החדשה אחר סוכות ע"ש.

In the book Kedushat Levi it is written that Chanuka is the beginning of the festivals in the new year after Sukkot.

The Sefat Emet cites the Kedushat Levi, who views Chanuka as initiating a new spiritual cycle of sacred days following Sukkot.

והיינו שהוא חינוך לכנוס ע"י קדושת חנוכה ופורים להג' רגלים.

Meaning that it serves as an initiation, through the holiness of Chanuka and Purim, for entering into the three pilgrimage festivals.

Chanuka and Purim prepare and sensitize the soul so it can later receive the deeper sanctity of Pesach, Shavuot, and Sukkot.

ולפי"ז נראה כי מקודם שהיו בנ"י במעלה עליונה היו יכולין לקבל הג' רגלים כמו שהם.

According to this, it seems that originally, when Israel was on a higher spiritual level, they were able to receive the three festivals as they were.

Before spiritual decline, the people had the capacity to enter directly into the holiness of the major festivals without preliminary stages.

ואח"כ שירדנו הוסיף לנו השם ית' הארת הימים הללו לזכות על ידיהם כנ"ל.

And afterward, when we descended, God added for us the illumination of these days so that we may merit through them, as explained above.

Chanuka and Purim were given as additional lights to compensate for diminished spiritual strength, enabling access to the holiness of the pilgrimage festivals.

Summary: Chanuka and Purim function as preparatory lights added after spiritual decline so that Israel can still reach the holiness of the three pilgrimage festivals.