I’ve heard some people conjecture that the word “Haftarah” is related to the word “Torah”, since it sounds similar and it immediately follows the Torah service in the Shabbat morning prayers. However, Rabbi S. R. Hirsch writes that the word “Haftarah” is based on the Hebrew root for “parting” or “taking leave” (peh, tet, reish). With the Haftarah reading, which consists of a selection from the writings of the Prophets related to the weekly Torah portion, we “take leave” and conclude the Shabbat morning prayer service called “Shacharit”. We follow this in the synagogue with an additional prayer service called “Musaf”, which literally means “addition”.
The historical origin — when and why — of reading the Haftarah is actually a bit of mystery! There are a few reasons offered as to when and why the Haftarah was instituted to be read. And the when and the why are also interrelated.
Two classic sources, the Avudraham and the Levush, are of the opinion that the custom began during the Greek occupation of the Land of Israel. (Think Chanukah!) At that time the Greeks prohibited reading the Torah in public. In reaction, our Rabbis instituted reading a portion from the Prophets each week (in place of the banned Torah reading), a portion that had a connection either to that week’s Torah reading or to a special event related to the time of the year in the Jewish calendar. Based on this opinion, reading the Haftarah began approximately in the year 450 BCE.
However, there are authorities who are of the opinion that the Haftarah reading was introduced at the time of Ezra the Scribe, around the time of the destruction of the First Temple. According to this, the Haftarah was instituted approximately 2,000 years ago.
There are numerous customs related to the Haftarah, and sometimes there are different Haftarah readings in Ashkenazic and Sephardic communities. Two main, widespread customs are that a “bar-mitzvah boy” is called to read the Haftarah and its blessings (before and after the reading), and also a groom reads the Haftarah. The latter custom is called (in Ashkenazic communities) “Aufruf”. In both cases, the one who is called to read the Haftarah also (re-)reads the last few verses of the weekly Torah portion, an aliyah that is referred to as “Maftir”. (Which also means “taking leave” from the Torah reading as explained by Rabbi Hirsch.)