On a test paper, the question was 'What is the Talmud?'  

The answer given was 'It is the exegesis (explanation) of the Torah, consiting of the collected works of the Mishnah'.

This is a fair, brief answer, but the student was bright and keen to understand more, and elsewhere more comprehensive, so I took the opportunity to set out in more detail the differences between 'Biblical' and 'Rabbinic' Judaism. 

The Talmud is not exactly 'the exegis of the Torah', though that's what the Rabbis want you to think!  Torah (and Te'NaKh more widely - this is the whole Hebrew bible which is pretty much the same as teh Christian 'Old Testament', a term we don't like and don't use because it implies that it has been superceded by the new one!) are the great written works of the Biblical period ('Israelitism', centralisation, hereditary, selected minority as priests, sacrifices).

From the crisis and trauma of the destruction of the first Temple (586 BCE - Before the Common Era - equivalent to BC - but we don't think Jesus was any more or less a child of God than the rest us, and don't accept him as 'Christ' - annointed or chosen one - so we don't date by 'Before Christ') to that of the second (70 CE, Common Era, equivalent to AD but we don';t acceoty Jesus as lord so we don't say 'year of our lord'), a new, non-hereditary, non centralised, non sacrificial, peer-led, 'REFORMED' and 'LIBERAL' interpretion of the inherited stories and traditions was needed, and thus was 'Rabbinic Judaism' born and ready to step in and take over when the romans destroyed the Temple (but another variant also stepped up, and eventually separated to become Christianity!).  Because the new leaders of this 'Rabbinic tradition' (the Rabbis) needed authority on which to claim leadership and interpretation, they developed the story that when God gave the written Torah, an 'oral Torah' was also given - how the Torah laws should be applied... and without which the Torah was pretty useless as a rule book.  (Another group, the Karaites, disagreed and thus rejected the Rabbis rulings - though in fact they also made their own, since often Torah rules were unclear, insufficient or contradictory).   They said (and pointed out) that the oral law had never been written down (I wonder why not?!) - and should never be (this is a great idea as it allows for flexibility, adaptation and development to the needs of the times etc).  

Sadly, in about 220, Rabbi Judah HaNasi (often simply known as Rabi) gathered the teachings of the Rabbis - usually based on - or at least 'hooked on to' the written Torah, and wroite it down.  This is the Mishnah - the first (written - and hence fixed) Rabbinic text.  As soon as that was copies and distributed, a wide variety of questions were raised about it (where it seemed its own rulings were unclear, insufficient or contradictory!) and that process of study and debate and argument continued for several hundred years - in two places, Tiberias (they weren't allowed to live in Jerusalem), and Babylon, and two colections were eventually produced - known as the Talmud (the Palestinian or Yerushalmi, which was stopped a hundred years earlier and is incomplete) and the Babylonian or 'Bavli' which became the authoritative version. So basically the Talmud is the great and major work of the Rabbinic period.  (Several hundred years later, after various scholars had continued this process even around the Talmud once it was published, Maimonides came along and decided to 'cut to the chase' and draw out all the salient conclusions' without the citations and tirtuous and lengthy debates, and produced teh Mishneh Torah, for which he was castigated and his books burned - but which are now core subjects of study in many yeshivas for advanced Jewish learning - see Maimonides in this blog).