The high holidays are early this year, 11 days earlier than last year; but that's OK because next year they'll be a month late. It's a funny thing about the Jewish holidays: they're either early or late but never just on time. It could be worse: consider the Moslems. This year the month of fasting, Ramadan, starts on October 14, 11 days earlier than last year; next year it will start on October 3; the next year - September 22; then September 11... and so on through the year, coming full circle in about 32 years. The Moslems have a fully lunar calendar, 12 months of 29.5 days, yielding a year of 354 days, 11 days shorter than the solar year. Thus, no Moslem holiday is connected to any season in the solar year, as over a 32 year cycle, every holiday falls in every season.
While the Jewish calendar is also based on a lunar month, our major holidays are based on the seasons, on the agricultural cycle of Eretz Yisrael. It would be absurd for Pesach to fall in the fall, or Sukkot in the winter. Therefore, we make a correction every two or three years, adding a month to compensate for the accumulated difference between the lunar and solar cycles. Such leap years occur in a fixed order, seven years out of every 19. That means that your Hebrew and Gregorian birthdays should be the same on your 19th, 38th etc. birthdays.
As in the case of the determination of the new moon, there was a time when the decision to add a month was not set and systematized, but was based on observation:
"Our rabbis taught: A year may be intercalated on three grounds: on account of the premature state of the grain crop, or that of the fruit trees, or on account of the lateness of the equinox. Any two of these reasons can justify intercalation but not one alone.
[but, once Rabban Gamaliel the Nasi wrote to the Diaspora communities:]
We beg to inform you that the doves are still tender and the lambs still young, and the grain has not yet ripened. I have considered the matter and thought it advisable to add thirty days to the year."
--Talmud, Sanhedrin 11b
In other words, if in Adar the spring seemed to be yet too far behind - if it appeared that the barley would not be ripe for harvesting by Pesach - then Nisan was delayed by adding another month between Adar and Nisan (called Adar II). And lest you say that that sounds a bit iffy, note that one of the criteria is the equinox, a marker of the solar year that is in no way related to climate. Thus, there was an absolute criterion to make sure that the Jewish calendar stayed in synch with the solar year.