In general they try to imitate how neurons and synapses work. For a complex model that means you are chaining neurons by connecting them with synapses. read more
To model a brain you would need to gain knowledge on how the neurons get connected. It is like creating a map of where neurons get chained to which other neurons, repeating. Think of it like this: if you try to connect 1000 neurons to each other, that requires an amount of more than 500000 Synapses. It's a simple summation. read more
Training a neural network model essentially means selecting one model from the set of allowed models (or, in a Bayesian framework, determining a distribution over the set of allowed models) that minimizes the cost. read more