Yuga refers to a large unit of time, era, or epoch. There are four Yugas that happen sequentially, and the four of them collectively loop, creating an endless loop of time.
Timing of the Yugas
When describing the length of the yugas or ages, and which yuga we are in and how far along we are in it, there is sometimes confusion about how to calculate them. The problem is when they are figured only according to years of earth's time, they will never be accurate. They are described in the Vedic literature according to the celestial years, or years of the devas. Nonetheless, there are specific references in the Vedic texts which make it clear how to calculate them. For starters, the Mahabharata explains it in detail:
The rishis, measuring time, have given particular names to particular portions [of time]. Five and ten winks of the eye make what is called a Kastha. Thirty Kasthas make what is called a Kala. Thirty Kalas, with the tenth part of a Kala, make a Muhurta. Thirty Muhurtas make one day and night. Thirty days and nights form a month, and twelve months form a year. Persons well-read in mathematical science say that a year is made up of two solar motions, meaning the northern and southern. The sun makes the day and night for men. The night is for the sleep of all living creatures, and the day is for work. A month of human beings is equal to a day and night of the departed manes [ancestors who have gone on to the subtle worlds]. That division consists in this: the light half of the month is their day which is for work; and the dark fortnight is their night for sleep. A year (of men) is equal to a day and night to the gods [devas or celestials]. This division consists in this: the half year for which the sun travels from the vernal to the autumnal equinox is the day of the gods, and the half year for which the sun moves from the latter to the former is their night. [Thus, an earth year is but a day for the devas.] Calculating by the days and nights of human beings about which I have told you, I shall speak of the day and night of Brahma and his years also. I shall, in their order, tell you the number of years, that are for different purposes calculated differently, in the Krita, the Treta, the Dvapara, and the Kali Yugas. Four thousand celestial years is the duration of the first or Krita age. The morning of that cycle consists of four hundred years and its evening is of four hundred years.
This says celestial years, or years of the demigods on the higher planets. Such years are much longer than those of planet earth. So 4000 celestial years, with the morning or Sandhya of 400 celestial years and the evening or Sandhyansa, or intermediate period, of another 400 years, equals 4800 celestial or divine years and 1,728,000 human years.
Regarding the other cycles, the duration of each gradually decreases by a quarter in respect of both the principal period with the minor portion and the conjoining portion itself. These periods always keep up the never-ending and eternal worlds. 
This means that as each age appears, from the Krita, Treta, Dvapara to Kali, each yuga decreases by a quarter of the previous yuga, in addition to the conjoining Sandhya and Sandhyansa periods with each yuga. In this way, it is roughly calculated that a whole cycle of the four yugas, namely Krita, Treta, Dvapara and Kali-yuga together, total about 12,000 celestial years in length.
The Mahabharata continues:
The learned say that these 12,000 celestial years form what is called a cycle. A thousand such cycles form a single day of Brahma. The same is the duration of Brahmas night. With the beginning of Brahma=s day the universal entities come into being. During the period of universal dissolution the Creator sleeps in Yoga-meditation. When the period of sleep expires, He awakes. What is Brahma's day covers a thousand such cycles. His night also covers a thousand similar cycles. They who know this are said to know the day and the night. On the expiry of His night, Brahma, waking up, modifies the indestructible intelligence by causing it to be overlaid with ignorance. He then causes Consciousness to spring up, whence it originates Mind which is at one with the Manifest.
In calculating the duration of the different yugas, there are a few differences between the Puranas. The Brahmanda Purana specifically states that Krita or Satya-yuga is 1,440,000 human years in length, Treta-yuga is 1,080,000 years, Dvapara-yuga is 720,000 years, and Kali-yuga is 360,000 years in length. The Linga Purana also agrees with this except for Treta-yuga, which it says is 1,800,000 years in length.
However, when explaining the various measurements of time, the Vishnu Purana, Bhagavata Purana, Bhagavad Gita, Vayu Purana, Mahabharata, and others agree on the measurements of the durations of the yugas, as explained below.
In the explanations of the measurements of time found therein, one cycle of the four yugas together is 12,000 years of the demigods, called divine years. Each of these years is composed of 360 days, and each of their days is equal to one human year. So Krita-yuga is 4000 divine years in length, Treta-yuga is 3000 divine years in length, Dvapara-yuga is 2000 divine years in length, and Kali-yuga is 1000 divine years long, with the addition of the conjoining portions of the Sandhya and Sandhyansa.
In this way, each yuga is preceded by a period called a Sandhya, which is as many hundred years in length as there are thousands of years in that particular yuga. Each yuga is also followed by a period of time known as a Sandhyansa, which is also as many hundreds of years in length as there are thousands of years in the yuga. In between these periods of time is the actual yuga. Therefore, we have:
Krita-yuga = 4000 divine years, Sandhya = 400 divine years, Sandhyansa = 400 divine years. Total = 4800 divine years x 360 days = 1,728,000 human years.
Treta-yuga = 3000 divine years, Sandhya = 300 divine years, Sandhyansa = 300 divine years. Total = 3600 divine years x 360 days = 1,296,000 human years.
Dvapara-yuga = 2000 divine years, Sandhya = 200 divine years, Sandhyansa = 200 divine years. Total = 2400 divine years x 360 days = 864,000 human years.
Kali-yuga = 1000 divine years, Sandhya = 100 divine years, Sandhyansa = 100 divine years. Total = 1200 divine years x 360 days = 432,000 human years.
This equals 4,320,000 human years in one cycle of the four yugas together, and 1000 cycles of these yugas equals 12,000 divine years and 4,320,000,000 human years in a day of Brahma.
Other Notable References
- Timings of the Four Yugas by Stephen Knapp