The word Talmud comes from the root "l-m-d" which means to learn or to teach.
The Talmud is the collection of Jewish laws and traditions, consisting of the Mishnah and the Gemara. Mishnah is the section of the Talmud consisting of the collection of oral laws, edited by Rabbi Judah ha Nasi (A.D. c135-c210).
For the following 300 or so years, the Mishnah was discussed, debated, and generally explicated, resulting in another, much longer body of text called the Gemara. Built to a large extent in question and answer style, it consists of both laws and stories (called aggadot).
After the Bible, the Talmud is the most important Jewish text.