The formal definition of the Talmud is the summary of oral law that evolved after centuries of scholarly effort by sages who lived in Palestine and Babylonia until the beginning of the Middle Ages.
It has two main components: the Mishnah, a book of halakhah (law) written in Hebrew; and the commentary on the Mishnah, known as the Talmud (or Gemarah), in the limited sense of the word, a summary of discussion and elucidations of the Mishnah written in Aramaic-Hebrew jargon.
This explanation, however, though formally correct, is misleading and imprecise.
The Talmud is the repository of thousands of years of Jewish wisdom, and the oral law, which is as ancient and significant as the written law (the Torah), finds expression therein.
It is a conglomerate of law, legend, and philosophy, a blend of unique logic and shrewd pragmatism, of history and science, anecdotes and humor.
It is a collection of paradoxes: its framework is orderly and logical, every word and term subjected to meticulous editing, completed centuries after the actual work of composition came to an end.
Yet it is still based on free association, on a harnessing together of diverse ideas reminiscent of the modern stream-of-consciousness novel.
Although its main objective is to interpret and comment on a book of law, it is, simultaneously, a work of art that goes beyond legislation and its practical application.
And although the Talmud is, to this day, the primary source of Jewish law, it cannot be cited as an authority for purposes of ruling.
–Rabbi Adin Steinsaltz
From The Essential Talmud by Rabbi Adin Steinsaltz