The exact date of the origin of the Coptic calendar is unknown, but it is believed that Imhotep, the supreme official of King Djoser C.2670 BC was the one who first created the old Egyptian calendar, thus it is the oldest in history that was originated three millennia before Christ. The Egyptians were the first to construct a solar calendar. They first formed a solar year of twelve months of thirty days each, plus one small month comprising five days only. Their year began with the heliacal rising of the star "Sirius", which usually occurred at the beginning of the Nile flood season. The civil year of that era had only 365 days, though Egyptian scientists had recognized the true duration of the solar year. However, in the meantime, they knew an astronomical calendar which is based on an astronomical concept of the heliacal rising of a bright star called Sirius "Canis Major, the Dog Star", at the dawn of the eastern horizon. They called it 'Spdt' or 'Sotis'. The day on which the heliacal rising of Sirius occurs marks the first day of the year. +
Sirius or Spdt lies about 8.6 light years from earth. The first day coincides with the arrival of the highest point of River Nile flood at Memphis. Ancient Egyptians realized that the heliacal rising of the star Sirius, or Sothis, coincides with the new year's day of the civil calendar, precisely every 1460 years. Some sightings were recorded in the 7th year of the reign of King Senusert III (1878-1841 BC). The dating of the event was the sixteenth day of the fourth month of the second season. The first day of the Egyptian Civil Year coincided with the heliacal rising of Sirius, marking the end of a Sothic cycle.
Also a record exists by the 3rd century AD grammarian Censorinus who noticed that, in AD 139, the first day of the Egyptian Civil Year coincided with the heliacal rising of Sirius. This phenomenon was celebrated by issuing coins, on the back of which appears the Greek inscription 'A ION', indicating an end of an Era. Discrepancies between the yearly Stellar cycle and Solar cycle were realized along the course of centuries or millennia. The difference is very slight, however, along the course of time it became visible and chaotic. The following Ancient Egyptian interesting stories illustrate the resulting effect of the widening gap. A record from an inscription from the reign of King Amenemhet III (1842-1797 BC) describes a visit of his treasurer Harurre to Serabit elKhadem, in Sinai, to extract turquoise ore in the third month of what was, according to the Civil Calendar, winter. The fact was, according to the inscription, the weather was that of high summer. Harurre describes how he and his men suffered badly from the mountains that brand the skin with the intense heat. The Civil calendar, then, was out of phase with Solar cycles by about seven months.
A papyrus of the Ramesside Period describes in the 13th century BC: "Winter is come in Summer, the months are reversed, the hours in confusion." It should be noted that ancient Egyptian Civil Calendar relates to regal years of each king and their Dynasties. By counting forwards and backwards the chronological order was then related to three heliacal risings of the star Sirus mentioned above. By the year 664 BC, the beginning of the Twenty-six Dynasty (Saite Period), the Egyptian chronology became more accurate. However, in spite of the stories mentioned above, the subdivision of the year into three seasons based on the regular River Nile flood and agricultural activities namely, inundation of the River Nile "Acht", sowing "Bert" and harvesting "Shemmo", remained accurately observed along the millennia. This subdivision possibly occurred during the Ramesside Period of the Nineteenth Dynasty. The Romans imitated the Egyptians in constructing a solar calendar.
The Egyptian scientist, Sosigenes, designed the Roman Calendar and Julius Caesar enforced it in the Roman Empire from the year 46 BC, in place of the lunar calendar. Augustus enforced the sixth intercalary day of the small month in the Egyptian calendar in 26 BC. The present Coptic Calendar Year was started on the 29th August, 284 AD, the acute time of Christian martyrdom. The solar year adopted in the calendar is eleven minutes and fourteen seconds longer than the precise average solar year. The difference has accumulated since the beginning of the Coptic Era causing a 13-day delay in the Coptic Calendar on the present time. The Coptic Christmas is on January 7th. The Coptic Year is the extension of the Ancient Egyptian Civil Year retaining its subdivision into the three seasons, four months each. This subdivision is maintained in the Coptic Calendar. The three seasons are commemorated by special prayers in the Coptic Divine Liturgy. The Coptic months are those inherited from their distant forbears of the Dynastic Period of Ancient Egypt. The farmers of the Coptic Period used them, and so do the Muslim farmers of present-day Egypt. The Feast of Neyrouz marks the first day of the Coptic Calendar known as the Year of the Martyrs "ANO MARTYRUM, A.M." Its celebration falls on the 1st day of the month named Tut, the first month of the Coptic Year, which usually coincides with the 11th day of September.
The Coptic Calendar has 13 months, 12 of 30 days each and an intercalary month at the end of the year of 5 or 6 days depending whether the year is a leap year or not. The year starts on 11 September in the Gregorian Calendar or on the 12th in the year before (Gregorian) Leap Years. The Coptic Leap Year follows the same rules as the Gregorian so that the extra month always has 6 days in the year before a Gregorian Leap Year. The names of the months and their starting dates are as follows: :Wout (Tout) 11-Sep 12-Sep Paopi (Baba) 11-Oct or 12-Oct A;or (Hator) 10-Nov or 11-Nov Aoiak (Kiahk) 10-Dec or 11-Dec Twbi (Toba) 09-Jan or 10-Jan Mesir (Amshir) 08-Feb or 09-Feb Paremhat (Baramhat) 10-Mar Varmoi (Baramouda) 09-Apr Pasanc (Bashans) 09-May Pawni (Paona) 08-Jun Epyp (Epep) 08-Jul Mecwry (Mesra) 07-Aug Pikouji'n'abot (Nasie) 06-Sep
You can get more information here.