The Home becomes a Beis HaMikdash, and you become the Kohen Gadol
The Midrash (Tanchuma, Behaaloscha) tells us that lighting the menorah is a greater merit than bringing korbanos. Hakodosh Baruch Hu said to Moshe to tell Aharon, "... When the Beis HaMikdash is destroyed, the korbanos will end, but your portion is to light the menorah, and that will remain forever." The Ramban (beginning of Behaaloscha) asks about this. When the Beis HaMikdash isn’t here, there is no mitzvah to light the menorah! "It must be referring to the mitzvah of Chanukah lecht, which continues after the Churban..."
The Yismach Yisrael (Bahalascha 4) says that we can derive from this Ramban that when one lights Chanukah lecht, he is like the kohen gadol lighting the menorah in the Beis HaMikdash. The simplest Yid becomes like a kohen gadol, and his home becomes a Beis HaMikdash.
We say in Al HaNissim בחצרות קדשיך נרות הדליקו, that the kohanim lit the menorah in the courtyards. The miforshim ask that the menorah was lit in the Heichel and not in the courtyard of the Beis HaMikdash!
The Sar Shalom of Belz zt'l answers that we are referring to the courtyards of every Jewish home. On Chanukah, one's courtyard (where he lights Chanukah lecht) becomes חצרות קדשיך, holy like the Beis HaMikdash.
