In this study site (Reach for the Bible), any reference to the term "extra-biblical" pertains to writings that are not included in the traditional protestant Bible as scripture but would have been familiar to both Jews and Christians of antiquity.
Many of these texts are historically and theologically useful for background studies of both the Old and New Testament.
Below are a few examples of some extra-biblical material we will be referencing in our more comprehensive studies.
Apocrypha
The Apocrypha is a collection of books included in the first Greek canon of the Old Testament and ancient Christian canons of the Old and New Testaments, but not included in the Masoretic Text of the Hebrew Bible. This collection consists of the following 14 books:
Epistle of Jeremiah
Tobit
Judith
3 Ezra
Additions to Esther
The Prayer of Azariah
Susanna
Bel and the Dragon
1 Baruch
Sirach (or Ecclesiasticus)
Wisdom of Solomon
1 Maccabees
2 Maccabees
Formerly 4 Ezra (also called "2 Esdras" or "The Apocalypse of Ezra") and the Prayer of Manasseh were considered a part of the Old Testament Apocrypha. However, they are not found in the oldest Greek codices, so these are now frequently and rightly considered among the books in the Old Testament Pseudepigrapha.
Pseudepigrapha
Pseudepigrapha is a term for the grouping of ancient writings set in the Old Testament period but written later (mostly between 200 BC and AD 200). These works often contain pseudonymous speeches of, or are pseudonymously ascribed to, biblical and deuterocanonical figures. Many of these texts are useful for background studies of the New Testament.
Charlesworth describes the Old Testament Pseudepigrapha as usually having the following features:
• They are Jewish or Christian.
• They are attributed to ideal figures in Israel’s past.
• They claim to contain God’s Word or message.
• They build upon Old Testament ideas and narratives.
• They were composed during the period 200 BC–AD 200 or preserve Jewish traditions that date from that period.
There are approximately 65 writings and fragments that qualify as Old Testament Pseudepigrapha according to these criteria.
Targum
Targum simply means ‘to translate’ or 'to explain'. In Biblical studies, it refers to the Aramaic translations of the Old Testament that were made, when Hebrew had ceased to be the normal medium of speech among the Jews. Some simply refer to 'Targums' as the 'Aramaic Bible'.
Midrash
The Midrash is a Rabbinic commentary of the Hebrew Old Testament texts, using different interpretive methods of study.
Talmud
The Talmud is a collection of rabbinic Jewish texts that record the oral tradition of the early rabbis. The Talmud is a primary source for the study of Judaism from the first century AD up to the date of its final redaction (as late as the seventh century). The Talmud is likewise relevant to the study of Judaism in Jesus’ and the apostles’ lifetimes.
There are two versions of the Talmud:
1. The Babylonian Talmud.
2. The Talmud of the Land of Israel.
The Babylonian Talmud is considered the most important collection of texts in rabbinic literature. It spans 2,783 folio pages in the standard editions. Although the collection takes the form of commentary on the Mishnah, the ancient rabbis included discussions and rulings on nearly every subject possible. Due to its incredible scope, the Babylonian Talmud became the fundamental text of Jewish life in the Middle Ages and for many people beyond this period.
The Talmud of the Land of Israel (also known as "Palestinian Talmud") was edited in Israel, prior to the editing of the Babylonian Talmud. However, it is much shorter and lacks the heavy editorial work that characterizes the Babylonian Talmud; thus, the Palestinian Talmud never gained the high position that the Babylonian Talmud has. Nevertheless, both Talmuds contain material from an earlier period and are also extremely useful for illuminating the background of the New Testament and early Christianity.
For more in-depth information on these extra-biblical sources, here are the sources I used to pick out excerpts:
The Lexham Bible Dictionary (Apocrypha, Pseudepigrapha, Midrash, Talmud)
The Oxford Dictionary of the Christian Church (Targum)
Connected study article: Gog and Magog – Ezekiel 38-39, Revelation 20 (Part 2)