Sukkah's lasting holiness in the home
Sukkos · sukkah · kedushah · dwelling · blessing
מצות הסוכת נותנת ברכה והארת קדושה לדירת האדם.
The mitzvah of the sukkah grants a blessing and an illumination of kedushah (holiness) to a person's dwelling.
Dwelling in the sukkah does not only fulfill a mitzvah for the moment; it draws down a lasting blessing and holy light into the place where a person lives.
וזה למען ידעו דורותיכם כיון שהמצוה בדירה נשאר ממנה ברכה לדירת האדם [מזוזה מלבר וסוכה מלגאו ]:
And this is the meaning of "so that your generations shall know" — since the mitzvah is performed in a dwelling, a blessing remains from it for a person's dwelling [the mezuzah is from without, and the sukkah is from within].
Because the sukkah is itself a "home," its kedushah lingers in our homes for all generations. The Sefas Emes contrasts the mezuzah, which guards the house from the outside, with the sukkah, which sanctifies it from within — the sukkah's holiness penetrates and surrounds the very space of our living.
Summary: The mitzvah of sukkah, because it is fulfilled in a dwelling, leaves an enduring blessing and inner kedushah upon a person's home for all generations — sanctifying the home from within, much as the mezuzah guards it from without.