Islamic calendar
The timing of the months in the Islamic calendar is determined by direct observation of the Moon. A new month can only begin after a "waxing crescent Moon" is observed shortly after sunset. The "waxing crescent Moon" is the phase of the Moon which starts right after a New Moon. A lunar month (one new moon to the next) lasts a little over 29.5 days. For convenience, a month is the Islamic calendar is either 29 days or 30 days, one after the other. So a 29-day month is followed by a 30-day month (29+30 is the same as 29.5+29.5). In most years, that means that a year of 12 calendar months last 354 days. But that "a little over" is 44 minutes every month so, to keep the calendar in step with reality, an extra day is needed nearly every third year, so these years are 355 days long.