A month is a unit of time measurement originally based on the changing phases of the moon. The lunar month - the time which the moon takes to complete one cycle of phases - is about 29.53 days long, and thus there are about 12.37 lunar months in one solar year.
Various calendars have adapted to this irregularity in different ways. The Gregorian calendar, and the Julian calendar from which it derived, have subdivided the year into twelve months varying from 28 to 31 days, and thus the timing of the moon's phases varies irregularly from month to month. The Maya calendar does not directly use a month related to the lunar cycle.
Many other calendars are luni-solar, and vary between 12 and 13 months in a year, so that the year is of irregular length. Since 235 lunar months are almost exactly 19 solar years long, a luni-solar calendar can be constructed which has 12 years of 12 months and 7 years of 13 months, which will keep the year relatively fixed to the solar cycle. The cycle of 19 years and 235 lunar months is called the Metonic cycle. The Hebrew calendar is based on the Metonic cycle.
The Islamic calendar is a purely lunar calendar with only 12 lunar months in a year, so the Islamic year is shorter than the solar year, and dates in the Islamic calendar drift relative to solar calendars and the seasons; 35 Islamic years are about 15 days shorter than 34 solar years.