The Age of Aquarius (and the Ages of Pisces, Aries, etc) are a way of describing the phenomenon of the precession of the Equinoxes. Traditional Astrology locates the vernal Equinox at the first degree of Aries. This was because around 4000 years ago the Vernal equinox did indeed occur against the zodiac background of the first degree of Aries.
However Earth's rotation around the Sun is not precisely one year and the vernal equinox does not therefore occur at exactly the same point in terms of zodiac longitude. Over time this difference grows. Approximately every 2200 years the Vernal equinox changes sign moving into the preceding sign, over 26000 years it completes an entire cycle of the Zodiac. So around 250 BCE the vernal equinox shifted into Pisces and some 2200 years after that date will shift into Aquarius.
Thus the Age of Aquarius is the time in which the Vernal equinox will occur in Aquarius and arguably bring an Aquarian slant to life. Just as the Pisces fish was a symbol of early Christianity and the Aries Ram a symbol of Egyptian religion (and in earlier times the cult of the Bull was drawn from a Taurean equinox), so the symbolism of the Water bearer will represent this 'New Age'. The individualism, interest in the unusual and off beat, the intrest in societyand human brotherhood are all Aquarian traits. Incidentally some of the activities identified as 'New Age' such as the use of drugs are far more Piscean (ruled by Neptune) than Aquarian. Peace and Love is also a Piscean rather than Aquarian concept (Pisces is a Water sign and more emotional than the airy Aquarius).
The problem with it is that no one actually knows when it will begin exactly. Some argue that it has already started, others that it will be another 100 years or so. This is partly because there is no exact point where the actual constellation of Pisces ends and that of Aquarius begins (moving backwards through the Zodiac). The constellations are not all the same size and clearly are separated by space which is difficult to allocate to one or the other.
Western astrologers have sidestepped the problem of precession by using the tropical zodiac. That is the first degree of Aries is defined as the Vernal equinox, rather than an actual zodiac backdrop. Vedic astrologers tend to use the 'sidereal' zodiac - or the actual background of the stars themselves. There is somewhere around 24 degrees difference between the two, so only if you were born in the last 6 degrees of a western sign do you have the same sun sign in both systems. For most people being born, say Libra under the Tropical system will mean that they are Virgo under the Sidereal system.
Hope this helps
Minderwiz