The Hebrew name for the Holy Temple is the Beit Hamikdash, the House of Holiness, a term that invokes a warm sentiment of a place where one is at home. It is therefore, perhaps, appropriate that one of the ways of mourning the loss of the Beit Hamikdash 2,000 years ago is to mark one’s home.
This specific custom is one of several referred to as zeicher l’churban, a remembrance of that which was destroyed (other commemorations include the practice of reciting Psalm 137 before the Grace After Meals and breaking a glass under the chuppah) It is written in the Talmud: “A man may stucco his house, but he should leave a little bare. How much should this be? Rabbi Joseph says, A cubit square; to which Rabbi Hisda adds that it must be by the door” (Talmud Baba Batra 60b).
To properly fulfill this custom, one who builds a new house should leave a one-cubit-by-one-cubit (about 18 inches by 18 inches) square of wall without paint, plaster or wall paper. There are some minority opinions that permit one to mark the zeicher l’churban by painting an appropriate size square a different color than the rest of the wall. If one purchased the house from a non-Jew, the walls do not have to be damaged to fulfill the custom unless one renovates the building.
As per Rabbi Hisda’s comment, the unfinished square is generally created near the entrance to the house, either above or opposite the door. This deliberate placement is to ensure that the unfinished square fulfills its purpose of being a constant reminder that the Beit Hamikdash, the natural home of the Jewish people, remains in ruins.