Indra is the Vedic deity associated with rain and thunder and lightning. The Rig-Veda has about 250 hymns to Indra. It is Indra's lightning that reveals the light of the sun and releases water to flow into the ocean.
Indra's Net conjures a beautiful and revealing image concerning a wide range of concepts and relations. I will leave it to "The Avatamsaka Sutra" to describe the image:
Far away in the heavenly abode of the Great God Indra, there is a wonderful net which has been hung by some cunning artificer in such a manner that it stretches out indefinitely in all directions. In accordance with the extravagant tastes of deities, the artificer has hung a single glittering jewel at the net's every node, and since the net itself is infinite in dimension, the jewels are infinite in number. There hang the jewels, glittering like starts of the first magnitude, a wonderful sight to behold. If we now arbitrarily select one of these jewels for inspection and look closely at it, we will discover that in its polished surface there are reflected all the other jewels in the net, infinite in number. Not only that, but each of the jewels reflected in this one jewel is also reflecting all the other jewels, so the process of reflection is infinite.
FRANCIS H. COOK: HUA-YEN BUDDHISM : THE JEWEL NET OF INDRA 1977
This idea is very powerful in a large number of different areas. I will try to give a good account of the more popular comparisons but as with any truly great idea, it can be found everywhere you choose to look for it.
Consider that each jewel represents a person. A tiny change in just one jewel will be reflected in every single other jewel, changing it. Each person, then, is merely a reflection of everyone else and the closer you are to a person the larger their reflection will be in you.
A generalisation of the above idea is to consider each jewel a thing, any thing. All things are connected and influence each other. Again, all things can only be defined in terms of other things and, were they solitary, would be dull and meaningless. This also suggests that the interactions of the things are what define them. What they are is merely their interaction with whatever is defining them.
Extending the idea again consider each jewel as an elementary particle. Feynman diagrams show how each particle can be shown to be the interactions of other particles. An electron, for example, can emit and re-absorb photons, but a photon can decay to an electron-positron pair which can then annihilate each other releasing a photon. The fact that an electron can be produced from a photon and a photon can be produced from an electron shows that there can be no lowest level and infinite regression is not only possible but required for the system to work.
The jewels are all reflections of each other stretching out infinitely in all directions. There can be no possible center or edge. Absolute position is meaningless. This line of reasoning can be applied over and over to destroy any notion of absoluteness in any form within Indra's Net.
I have already touched on this idea but there can be no self in the Net. Any self exists only as a reflection of all others. Conversely there are no others, just reflections of your infinite complexity.
Coming back to earth for a moment, you can consider Indra's Net as a hologram. All the information in the entire net is expressed in a single jewel just as the entire picture exists in a hologram's pixel.
The internet (and by implication E2) has also been suggested as an analog to Indra's Net. There is a high degree of connectivity and once you invoke the idea of chaos you can see that small changes in a far off website will given time effect the dynamics of the internet. So we have both interconnections and interdependence although you would have difficulty arguing that even E2 is a reflection of the entire internet.
The hallmarks to look for when drawing parallels with Indra's Net are interconnections, interdependence, infinite regression and information duplication. You will very likely find that these parallels will be revealing in themsleves as well as the parallels you can draw with other systems that are similar to Indra's Net (the parallel parallels if you like)
Douglas R. Hofstadter, Godel, Escher, Bach: an Eternal Golden Braid