According to the Bible, God gave the Jews the Tanakh — which Christians call the Old Testament. The Tanakh is composed of the Torah (the Pentateuch or the first five books of the Bible which give the law), the Nev'im (the prophets), and the Kethuvim (the writings). But the laws of the Torah can be hard to understand and often not very specific. In fact, the Old Testament contains passages that encourage explaining God’s Word (Deuteronomy 33:10; Nehemiah 8:7-8; 2 Chronicles 17:7-9). So Orthodox Jews believe God also gave Moses the Oral Law — a set of instructions that elaborate on the law—, and they compiled that into written form called the Mishnah. In addition, rabbis and scholars added their own explanations — some accurate, some merely speculation, and some contradictions. The extra explanations were compiled into the Gemara. These instructions in the Oral Law/Mishnah and the Gemara are in the form of short parables, or Midrashim.
Jesus and the apostles sometimes used a Midrash-like approach in explaining how the Old Testament points to Christ (Luke 24:27; Matthew 5:17; Galatians 3:16, 4:21-26). While the Midrash provides insight into rabbinic interpretations, it expands on Scripture, so it should never be considered on par with God’s inspired Word (Deuteronomy 4:2). Some Midrashim faithfully illuminate God’s Word, while others reflect cultural ideas or conflicting opinions; careful discernment must be used to distinguish the Midrash’s use as a valuable historical and contextual resource but not authoritative or inspired Scripture.
There are two basic categories of Midrashim: A collection of Midrashim on a single topic or book is also called a Midrash.
Midrash Halakhah
In Hebrew, halakhah refers to the law given in the Torah and the Mishnah. It includes the religious, ceremonial, and civil regulations. The Midrash Halakhah, then, gives explanation to those laws. The Midrash Halakhah is divided into the Mehkilta on Exodus, the Sifra on Leviticus, and the Sifrei on Numbers and Deuteronomy. They all give detailed explanations of the passages in the Torah, down to who is being referred to by which pronoun. They also attempt to explain why each law was brought into play.
For example, in the Shema in Deuteronomy 6:6-9, the Midrash Halakhah explains what is meant by "these words," "why you lie down and when you get up," and how you can wear the law between your eyes. The Midrash Halakhah was also essential in reinterpreting ceremonial law for a Judaism that had no Temple. Two different rabbinical schools compiled the three books. One school believed every word was intentionally placed and had the potential to develop into another law. The other believed that Scripture, like human speech, was subject to flourishes that didn't really mean anything.
Midrash Aggadah
Unlike the Midrash Halakhah, the Midrash Aggadah speaks more about stories, characters, and ethical dilemmas. Midrash Aggadah specializes in taking Scripture and teasing out a modern application. Several commentaries of a single passage may sit one after another, with no correct interpretation identified. Behind-the-scenes stories are added to explain terse and confusing accounts given in Scripture. The Midrash Aggadah is not meant to be literal Scripture — more jumping-off points for contemplation. They are still used today to explain such topics as feminism and the Holocaust.
The Midrash Rabbah is the most cohesive collection of Midrash Aggadah, although Midrash Aggadah are found throughout Jewish writings. The Midrash Rabbah is actually ten volumes, one each on the Torah and the five Megillot (Song of Solomon, Ruth, Lamentations, Ecclesiastes, and Esther). Each volume includes Midrash Aggadah gathered between the fifth and eighth centuries. "Rabbah" means "great" and identifies each book as the largest collection of Midrash Aggadah on the given book of the Tanakh, although other, smaller, collections do exist. A Midrash Aggadah could be a poem about a passage, a homily about an ethical consideration a passage mentions, or a story that explains the behavior of a character. Some reflect the difficult times in which they were written, and some seem to come out of nowhere.
Other Midrash
Other Midrashim collections do exist, such as those on 1 and 2 Samuel, the Psalms, and Proverbs. Others are topical and cover a variety of subjects.
Are the Midrashim accurate interpretations of Scripture? Some of them probably are. But there's no real standardization, and it would be easy for a Christian to get confused as to what is truth and what isn't. Second Timothy 3:16-17 says that all Scripture is inspired by God and suitable for instruction, and this certainly includes the Old Testament. But it doesn't include the descriptions, speculation, and stories of the Midrash.