Answer:
   
   The Jewish calendar is based on a lunar system in which each month
   begins at the new moon. A month can consist of 29 or 30 days.
   
   Originally the determination of the new moon was by the Sanhedrin
   (highest rabbinic court, 70 members) when witnesses declared that they
   had seen the new moon. Once the Sanhedrin declared the new month,
   messages were sent to the various communities stating which day (of
   the two possible) began the new month.
   
   Note that this does not say that the Sanhedrin did not know the
   methods of calculating the new moon, but merely that proper procedure
   required the witnesses. The astronomical calculations could be used to
   verify the validity of the witnesses, if necessary.
   
   In those months in which holidays occurred, (such as Nisan for
   Pesach), the exact date was critical for determining when the holiday
   began. Since the messengers could not reach every community in the
   time allotted, those communities they could not reach would celebrate
   both possible days.
   
   In 325 CE, the Byzantine (Eastern Roman Empire) administration in what
   was then Palestine limited the rights of the Sanhedrin to disseminate
   calendrical information. Hillel II, the Sanhedrin President at the
   time, published a set of rules for the maintenance of the calendar,
   which is still used today.
   
   The Sanhedrin also determined that those communities outside of Eretz
   Yisrael would continue to keep the second day of the holiday because
   of a principal "Minhag Avoseinu Beyadeinu", the customs of our fathers
   [remain] in our hands, and to remember the law for when the Sanhedrin
   is reestablished and the month is determined by witnesses again.
   
   Reform Jews believe that since the calendar is defined exactly, there
   is no longer a need to keep the second day of Yom Tov outside of Eretz
   Yisrael. However some Reform Jews do choose to observe two days.
   
   Many Orthodox Jews feel that once the Sanhedrin is reestablished, that
   the declaration will be disseminated by CNN [Cable News Network] or
   maybe even soc.culture.jewish, and even the Jews outside of Eretz
   Yisrael will only be required to keep one day. However, until that
   time comes, the requirement is to maintain the calendar as established
   by the original Sanhedrin, which includes two days.