What is Indra's Net, according to Mahayana Buddhism?

There are two sets of Mahayana sutras:

1. The seventeen Perfection of Wisdom sutras (Prajnaparamita Sutras), and
2. The other sutras, of the Wheel of Perfect Differentiation.

The first set does not present Indra’s net while the second does. Tibetan traditions posit the first set as being “of definite meaning” and therefore study it and overlook the second. They do not study the sutras of the Wheel of Differentiation except through commentaries refuting their presentations.

On the other hand, most Chinese, Korean, Japanese and Vietnamese traditions such as the Huayan school, Chan, Tientai, etc. posit the second set of sutras as being “of definite meaning” and therefore study it and overlook the Perfection of Wisdom sutras.

Therefore, if you want to know more about Indra’s net, you have to look on the side of Zen, etc. because they are more likely to comment sutras that speak of Indra’s net. Among the various sutras of the Wheel of Perfect Differentiation, the most well known are:

• The Lankavatara Sutra (remember that Chan masters were first called "Lankavatara masters" before the "Chan" designation came into being),
• The Avatamsaka Sutra (Garland of Flowers), that became popular after the Lankavatara was found too complicated for lay people
• The Lotus sutra,
• The Tathagatagarbha Sutra, and
• The Vimalakirti Sutra.

Most of them mention Indra (just as the Prajnaparamita Sutras do) but do not mention Indra’s net. For instance, the Vimalakirti Sutra merely mentions Indra. Even the translator's footnotes do not say more than:

21. Kausika, Sakra, and Indra all refer to the same god, who, in Buddhist cosmogony is regarded as the king of gods in the desire-realm.

This helps you understand that it is not that common a notion.

Of these scriptures, only the Avatamsaka Sutra (a 1’500 pages sutra) does. It says:

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 stars of the first magnitude. A wonderful sight to behold. If we now arbitrarily select one the 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 jewels is also reflecting all the other jewels, so that the process of reflection is infinite.

Thích Nhất Hạnh is a Vietnamese Zen master in the lineage of Huineng. The Caodong Chan school in China and the Soto Zen school in Japan also proceed from Huineng. In Understanding Our Mind (Chapter 13, Indra’s Net), Thích Nhất Hạnh refers to the Avatamsaka Sutra:

Indra's net is a vast, cosmic lattice that contains precious jewels wherever the threads cross. There are millions of ewels strung together to make the net, and each jewel has many facets. When you look at any facet of any jewels, you can see all the other jewels reflected in it. In the world of the Avatamsaka, in Indra's net, the one is present in the all, and the all in the one. This wonderful image was used in Buddhism to illustrate the principle of interdepedence and interpenetration.

And he explains the meaning:

In our ordinary world, we see a teapot as a single, independent object. But if we look deeply enough into the teapot, we will see that it contains many phenomena – earth, water, fire, air, space, and time – and we will realize that in fact the entire universe come together to make this teapot.

From this Vietnamese Zen perspective, this is analyzing dependent-origination.