This is a subtle notion which can be summarized as: no thing/event/action arises independently from any other — Indra’s net is a metaphor for dependent origination (pratityasamutpada). Working out what exactly dependent origination means takes up a lot of Buddhist philosophy. In English it is referred to by many other terms, including dependent co-origination, co-dependent origination, and Thich Nhat Hanh’s interbeing. Dependent origination is the basis for ethical action — hurting you, I am hurting myself.
For more information, see https://en.wikipedia.org/wiki/Pratityasamutpada.