A binyan av is a rule derived from a verse (or from two verses) that is applied to all cases that are similar to the one in the verse. Some examples:
* The permission to prepare food on Yom Tov was only stated in regards to Pesach. From a binyan av, we apply this rule to all similar days, i.e., Succos, Shavuos, etc.
* Deuteronomy 19:15 specifies that the testimony of “one witness” is inadmissible. From a binyan av, it is determined that any place the Torah says “witness” without such specification, it refers to testimony in general, which requires two witnesses.
* The Torah prohibits a man from marrying his sister, including a half-sister on his mother’s side. When the Torah discusses the prohibition against marrying one’s father’s sister, we know from a binyan av that this includes his father’s maternal half-sister.
The Talmudic term “tzad hashaveh,” meaning an aspect in common, is used to determine what cases are similar for the purposes of applying laws from one case to another. See Talmud Baba Kama 6a to see how the Sages analyzed the Torah’s cases of fire and a pit in the public thoroughfare in order to apply laws from those cases to other forces and obstacles that might cause damages.