The Vedic concept of time, like that of the ancient  Egyptians and the Mayans, was cyclical. As per their cosmovision, in addition  to the cycles of day and night, and the cycles of the seasons, there exists  another cycle of time known as the Yuga  Cycle or the Cycle of the World Ages.  The ‘Laws of Manu’ state that the Yuga Cycle is of 12,000 years duration, and  is comprised of four Yugas or World Ages – Krita or Satya Yuga (Golden Age),  Treta Yuga (Silver Age), Dwapara Yuga (Bronze Age) and Kali Yuga (Iron Age). As  humanity moves from the Krita Yuga to the Kali Yuga, the level of virtue and  human capabilities gradually decrease, and reaches its nadir in the Kali Yuga,  the age of darkness, in which we currently find ourselves.
However, sometime prior to 500 CE, some errors had  crept into the Yuga Cycle doctrine in many Sanskrit texts. The Yuga Cycle was  considered to be of 12,000 divine years’ duration, wherein one ‘divine year’ was believed to comprise of 360 ‘human  years’. The 12,000 years duration of the Yuga Cycle was, therefore, multiplied  by 360, thereby arriving at the abnormally high value of 4,320,000 years. The  fallacy of this approach was rectified by the renowned Vedic seer, Swami  Yukteswar. In the book The Holy Science (1894), Yukteswar clarified that a complete Yuga Cycle takes 24,000 years,  and is comprised of an ascending Yuga Cycle of 12,000 years when virtue  gradually increases (Kali, Dwapara, Treta, Krita) and a descending Yuga Cycle of  another 12,000 years (Krita, Treta, Dwapara, Kali), in which virtue gradually  decreases. 
The interpretation of Swami Yukteswar can be  intuitively understood, since everything in nature moves in ascending and descending  cycles. We know that the Babylonians, Egyptians, Mayans and the Incans all used  a daily time system that comprised of 12 ascending time periods (our AM) and 12  descending time periods (our PM) for a 24 hour day. In the cycle of the seasons  too, we can see that the intensity of sunlight gradually increases from winter  to summer for a period of roughly 12 lunar hemicycles (i.e. the time taken from  New Moon to Full Moon and vice versa), and then decreases from summer to winter  for another period of 12 lunar hemicycles.
The belief in the Yuga Cycle was widely prevalent in  the ancient world. Giorgio de Santillana, professor of the  history of science at MIT, mentions approximately thirty ancient cultures that believed in the concept of a series of  ages, with alternating Dark and Golden Ages, as documented in the book Hamlet's Mill (1969). The Persians,  Greeks, Romans, Celts, Hopi Indians - all have detailed accounts of the World  Ages which are surprisingly alike in their descriptions. The ancient Persians  believed that the world lasts for 12,000 years, at the end of which all the  hostile spirits are defeated. The twelve constellations of the Zodiac  controlled the months of the year, and each ruled the earth for a thousand  years at the end of which the sky and earth collapsed in chaos. The idea of a  12,000 year cycle was also prevalent amongst the Chaldeans. The Greeks believed  in a ‘Great Year’, also called a ‘Platonic Year’ or ‘Supreme Year of  Aristotle’, whose duration was variously represented as 12,954 years (Cicero)  or 10,800 years (Heraclitus). According to the Latin author Censorinus, in this  ‘Great Year’, there is a great winter or Kataklysmos (which means ‘deluge’) and  a great summer or Ekpyrosis (which means ‘combustion of the world’). We should  also remember that, although many Sanskrit texts describe the Yuga Cycle  duration as being of 12,000 divine years, certain texts, such as the epic Mahabharata (Vanaparva), still retain the  duration of the Yuga Cycle as 12,000 years.  
Interestingly, the complete Yuga Cycle of 24,000 years  closely matches the Precessional Year of 25,765 years, which is the time taken by the sun to ‘precess’ i.e. move  backwards, through the 12 zodiac constellations. In order to understand the  phenomenon of precession we need to remember that the 12 constellations of the zodiac encircle our Solar System like a  giant ring. As a result, the sun always rises each morning against the backdrop  of a particular constellation. If you consider a fixed date on our calendar,  say the Vernal Equinox date of March 21st, you will find that the  sun rises against the constellation of Pisces on this date. However, in a  couple of hundred years from now, the Vernal Equinox sun will rise against the  backdrop of Aquarius. There is a very slow movement of the heavens, because of  which the background constellations appear to move backwards i.e. ‘precess’  along the zodiac. The Vernal Equinox sun takes nearly 2,147 years to move  through each zodiac constellation of 30 degrees, and an entire cycle of 360  degrees is completed in approximately 25,765 years, known as the ‘Precessional  Year’.
In recent years, it has been observed that the rate of  precession is ‘increasing’, which means that the duration of the Precessional  Year is ‘decreasing’. The duration of the precessional cycle has dropped by  nearly 20 years in the past 100 years of recordkeeping. Indeed, if we assume  that the precessional rate will decrease at this rate for the next 12,000  years, then we would end up with a Precessional Year duration of close to  23,000 years. It is possible, therefore, that the current precessional value of  25,765 years is simply a cyclical deviation from its Mean Value, which is close  to 24,000 years. 
The ancient Sanskrit treatise on astronomy called Surya-Siddhanta, also gives us specific  information on precession. The text itself claims that the information within  it was revealed to the great asura named Maya by the Sun god himself, at the end of the Golden Age (Krita Yuga).  The asura Maya had performed great religious austerities for the Sun god, with  a desire to know the science upon which time is founded, namely the motion of  the heavenly bodies (jyotis). And as  per the information in the Surya Siddhanta, the precession of the equinoxes  takes place at the rate of 54 arc seconds per year  (as against the current value of 50.29 arc seconds per year.) This translates  into a Precessional Year duration of exactly 24,000 years! 
In addition to the Yuga Cycle, the Vedic texts also  tell us of another large cycle of time known as a ‘Day of Brahma’, also  referred to as a ‘Kalpa’, which is equal to a 1000 Mahayugas or Yuga Cycles.  The Vishnu Purana states that at the  end of a ‘Day of Brahma’ the physical universe is destroyed and is dissolved  into the waters of the Primordial Ocean. This is followed by a ‘Night of  Brahma’ which is of equal duration as the ‘Day of Brahma’, when no life forms  exist. At the end of the ‘Night of Brahma’, the universe is once again created  by Vishnu from unmanifested matter. This phenomenon of cyclic creation and  destruction events is also explained by Krishna in the Bhagavad Gita: 
“Those who understand the cosmic laws know that the  Day of Brahma ends after a thousand Yugas and the Night of Brahma ends after a  thousand Yugas. When the day of Brahma dawns, forms are brought forth from the  Unmanifest; when the night of Brahma comes, these forms merge in the Formless  again. This multitude of beings is created and destroyed again and again in the  succeeding days and nights of Brahma.” 
In order to derive the value of a ‘Day of Brahma’ we  need to remember that as per the Vedic texts, the Yuga Cycle (also known as a  Caturyuga or Mahayuga), consisting of the four Yugas, is considered to be of  12,000 years duration, which is half the duration of the Precessional Year.  Therefore, a ‘Day of Brahma’ lasts for 12,000*1000 i.e. 12 million years, which  is followed by a ‘Night of Brahma’ of equal duration. The implications are  fascinating: all life forms on the planet earth are extinguished after 12  million years!  These life forms then  remain in a dormant, unmanifested form for a further 12 million years. And  then, at the beginning of the next ‘Day of Brahma’, new life forms are brought  forth by the creative process from unmanifested matter.
Thus, we have a cyclical 24 million year period of  cosmic creation and dissolution, much like the 24,000 year Precessional Year,  and the 24 hours of day and night. The essential similarity between the  macrocosm and the microcosm couldn’t be any clearer! It is easy to see that the  time period between two successive cosmic dissolution events is 24 million  years. It occurred to me that if this information is correct, then this cycle  of creation and destruction should also be reflected in the fossil records of  the planet earth. And amazingly enough, this is exactly what has been revealed  by recent paleontological evidence: every  26 million years there is a mass extinction of species on the earth!
Consider this: 66 million years ago the dinosaurs were  thriving on the earth. However, today we can only find their bones and fossils  in natural history museums. What happened to them? Scientists believe that 65.5  million years ago the earth went through a period a rapid death, called a mass extinction. But this episode is not  the only mass extinction event in the fossil record. There are many more. And  in recent years paleontologists have suggested that these mass extinctions  occur in a regular cycle. 
  
    |   | Fig 1: Stegosaurus fossil in the Field Museum, Chicago. Source:    Wikipedia Commons  | 
   Surya-Siddhanta:a text-book of Hindu astronomy,  Ebenezer Burgess, Phanindralal Gangooly, Chapter 1, p 1
      The Bhagavad  Gita 8.17-8.20