The Jerusalem Talmud, also known as the Talmud Yerushalmi, and sometimes incorrectly referred to as the Palestinian Talmud, was written as a
commentary on the
Mishna. Between the years 225 and 375, semi-concurrently with the
Bavli, or Babylonian Talmud, but slightly before, the Jerusalem Talmud was composed: at first in
Caesaria and later in
Tiberias. This Talmud is less studied than the Babylonian Talmud, and contains commentary on fewer tractates of the
Mishna, and is currently approximately 1/3 the size of the Bablyonian Talmud, because segments have been lost since the time of its redacting.
The Jerusalem Talmud is the de-facto Authority, however, in two areas, where the Babylonian Tamud does not exist: laws of Agriculture in the land of Israel, and the laws of ritual purity, neither of which were ever practically aplicable outside of the land of Israel.
Modern Scholars disagree about the reason why much of the material was lost. The first group claims that first, there was a consensus that the Jerusalem Talmud was compiled hastily and in a more terse, haphazard fashion than the Bavli, due to the stress that the rapidly failing Jewish community in Israel was facing. This lack of acceptance led to a rejection, in terms of how we decide the Halacha, which therefore led to the Jerusalem Talmud being studied less than the Bavli. Being less studied, there were fewer copies in existance, and despite strong evidence that the Rambam had copies of tractates we now do not have, it is not even know which tractates existed before the repeated anti-semitic purgings and burnings of the middle ages.
The second group of Scholars believe the reverse to be true: The fact that much of the Jerusalem Talmud was lost, or less well known, was the cause of its neglect, and therefore Rabbis did not study it as much, and it became more and more neglected as separate Halachic works began to appear, which ignored this lesser known talmud.
In either case, the Jerusalem Talmud has become more widespread as more in-depth study of Halacha and the Babylonian Talmud has increased in the last thirty years, especially in Israel.
Note
Some more recent commentators have called into question the factual nature of certain claims made above, vis-a-vis the rejection of the Talmud Yerushalmi as a Halachic source. These people claim that the Rambam followed the ideas of the Yerushalmi over the Bavli, where conflicts existed. While not being able to judge these claims myself, many people I have asked have been able to list many counter examples, and the Introduction to the Rambam's Magnum Opus, the Yad Chazakah (or Mishna Torah) he states explicitly that the Law follows the Bablyonian Talmud.
Sources
A guide to the Jerusalem Talmud, by Heshey Zelcer. www.brownwalker.com/upb/pdf-b/1126301b.pdf
Aish Hatorah's Crash Course in Jewish History, the Talmud, by R. Ken Spiro. http://www.aish.com/literacy/jewishhistory/Crash_Course_in_Jewish_History_Part_39_-_Talmud.asp