Today is the 2nd day of Adar, 5770
Our months follow the actual cycle of the moon –new moon, full moon, etc- which consists on 29,5 days. Therefore, on average, Hebrew months will have 29 days and the next 30 and so on. A lunar (=moon based) year -12 lunar months- will have therefore 354 days (12×29.5).
There is a special Mitzvah in the Torah that says: “Shamor et Chodesh ha-Abib” which instructs us to keep the holiday of Pesach specifically on spring season. Now, if we would follow exclusively the lunar calendar, Pesach would fall at different seasons, because of the 11 days gap between the lunar and the solar year (354/365).
In order to ensure that Pesach would always fall during the spring season, these two calendars must be coordinated. How do we do that? Adding an additional month -a thirteenth month- to the year. A year that has 13 months is a called a leap year (shana me’uberet).
To summarize: The Hebrew calendar is lunisolar (=moon and sun) with a thirteenth month which is added to adjust the two calendars. This extra month is called Adar Alef (first Adar) and is added before the “real” Adar which is the one that comes immediately before Nisan and is called Adar Bet (second Adar). According to the Hebrew calendar calculation cycle this extra month is added seven times every nineteen years (specifically, in years 3, 6, 8, 11, 14, 17, and 19).
5770 is NOT a leap year, it has only one Adar.