There are a number of types and styles of artificial intelligence[1], but there's a key difference between the branch of programming that looks for interesting solutions to pertinent problems, and the branch of science seeking to model and simulate the functions of the human brain. Neuromorphic computing, which includes the production and use of neural networks, deals with proving the efficacy of any concept of how the brain performs its functions -- not just reaching decisions, but memorizing information and even deducing facts.
Both literally and practically, "neuromorphic" means "taking the form of the brain." The key word here is "form," mainly because so much of AI research deals with simulating, or at least mimicking, the function of the brain. The engineering of a neuromorphic device involves the development of components whose functions are analogous to parts of the brain, or at least to what such parts are believed to do. These components are not brain-shaped, of course, yet like the valves of an artificial heart, they do fulfill the roles of their organic counterparts. Some architectures[2] go so far as to model the brain's perceived plasticity (its ability to modify its own form to suit its function) by provisioning new components based on the needs of the tasks they're currently running.
Also: A neuromorphic, memory-centric, chip architecture[3]
The goals of neuromorphic engineering
While building such a device may inform us about how the mind works, or at least reveal certain ways in which it doesn't, the actual goal of such an endeavor is to produce a mechanism that can "learn" from