Substrate independence denotes a property being separable from its physical implementation. One could say Alan Turing showed that computation is substrate independent, since many machines all do the same sort of computation. It's often debated whether consciousness is substrate independent, whether a piece of silicon just simulating a human brain will actually have an internal experience of its own thoughts. People who believe in souls, dualism, or panpsychism tend to think it isn't (to different degrees), people who believe in reductionism or emergentism tend to think it is. The authors of this piece go so far as to say the stuff the brain does might not even be reproducible outside of flesh-and-blood, regardless of whether such a reproduction would have internal experience.
If I recall my terms correctly, substrate independence is the idea that creating intelligence is not dependent on using neurons, but that if you could model the required functionality of neurons in another substrate, an intelligence could also be housed in that substrate.
> Neuromorphic computing Is basically modelling neurological architectures in computers.