And you guys are hitting on a potential positive about having the software running outside of the hardware. It is easier for updates to the knowledge base of the network. MS will most likely work with developers on the software and provide updates when necessary since each game disc will most likely have the data on it.
A neural network is basically a series of weighted nodes that take a set of inputs and output a set of output value(s). Training the network alters the weights of the nodes until an acceptable accuracy is achieved for all input sets. I did a neural network in college where the inputs(actually, the input names are irrelavent since it was just float values, the network could handle any number of inputs and any number of expected outputs) were enemy distance, ammo, health, and weapon and the outputs were attack, defend, or stay. For training purposes you provide the inputs with the expected outputs and let the system keep iterating over the training sets and altering node weights until each set is met with an acceptable outcome.