The name comes from the Akkadian Addaru, one of the Babylonian month names adopted wholesale into Hebrew usage. The month runs a fixed 29 days in every year.
The month names are Babylonian. Twelve of them are the Akkadian month names taken into Hebrew during and after the exile, and the biblical books of the return use them freely while the earlier books generally number the months or use a small set of older Canaanite names. The atlas records the borrowing rather than presenting the names as native, because it is one of the clearest visible marks the exile left on Jewish practice.
The Jewish calendar as now kept is calculated rather than observed. Month lengths are fixed by rule except for Cheshvan and Kislev, which absorb the adjustment and may run 29 or 30 days, and a thirteenth month is added in seven years out of nineteen on a fixed cycle so that Passover stays in the spring. A further set of rules, the postponements, shifts Rosh Hashanah off certain weekdays, which is why the year has six possible lengths rather than two.
Adar contains Purim on the fourteenth. In a leap year this month becomes Adar I and runs 30 days, and Purim moves to the added month, Adar II, so that it stays adjacent to Nisan and Passover. The doubling therefore falls on the month before the festival rather than after it.