This is from my exploration into neuroscience. This multidisciplinary field is forcing me into reading varied texts across the academic spectrum. I have only touched the surface so this is a surface level over reductionist summary of what Hopfield is.
Hopfield networks, named after its inventor, is a type of recurrent and cycling neural networks that is able to “Remember” and retrieve certain types of stored information.
It is made up of single layer of interconnected neurons, with each neuron connected to Every other neuron in the chain.
The network is trained by presenting it with set of input patterns, which it then “Learns” by adjusting the strength of connection between neurons ( increase in NT release sensitivity at the synapse).
Once the network is trained it can be presented with new patterns and it will attempt to recall the most similar stored pattern – As strength of connection is variable after learning.
Understanding of this network is important for understanding the functioning of brain. Brain has learnt circuits that fire up when presented with pattern of inputs – like your partner slapping you is a sequence of inputs.
This network is also used for error correction and optimization in varied computer related application but those are beyond me for now.
Drmd 
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