If you fly into Delhi's Terminal 3, you'll see this: a big installation of hasta-mudras (hand-symbols) as you come down the escalator in the arrivals area.
Like all human gestures, these hastra-mudras are primarily meant for communication. Each one has a meaning and a way of usage.
The language of mudras was once understood by all Indians; but unfortunately, it has now become an esoteric piece of knowledge, understood only by specialists. The typical visitor to the airport walks past these hands thinking, ah, ok, ummm, mudras, yes, very good, very good, great Indian traditions, yes, yes, very good indeed :) :)
But what do these mudras mean?
An explanation for these symbols can be found in the Natyashastra, a classical manual on the theory and practice of Indian aesthetics (theatre, music, dance, poetics, etc). Based on linguistic analysis and references, scholars date the Natyashastra anywhere from 2nd century BCE to 2nd century CE.
Chapter 9 of the Natyashastra explains 67 types of mudras, dividing them into those using a single hand, and those requiring two hands. It also explains general rules regarding their usage, how the arms are to be moved, the "quantity" or extent of gesturing to be done, etc.
For example, the symbol in the photo here is called "tripataka". Pataka = flag, and tripataka = flag with 3 fingers.
The tripataka mudra can be used for crowning a king; for example, with both hands in tripataka, you can depict the placement of a crown on someone's head.
This mudra is used for anointing someone's forehead with a tilaka. This mudra, with the finger pointing downwards and hand moving up and down is used to represent the flight of a small bird, or the movement of a stream or of a snake.
It is used for raising up something; for example, if you are giving blessings to someone who has fallen at your feet, you can raise the person using two hands in tripataka.
With two tripataka hands facing each other, you can represent a door. You can use it to wipe off tears.
It has more exotic uses as well - for example, if you want to depict an underwater fight between two monsters, you can use tripataka! The jumping of monkeys is also represented using tripataka.
As you can see, a single mudra is used in different ways and combinations, to create different meanings. Traditional classical dance performances in India usually use these gestures as part of their vocabulary.
One of the major reasons why classical dances lose out to 'modern' dance is the loss of this vocabulary. Over the years, the audiences no longer understand the gestures, and a vital link between performer and audience has been lost. A painstaking re-education is the only way to revive it. It's either that, or resign ourselves to losing these traditions.