I am certainly not an expert, but I can post some relevant information to a couple of these questions.
Jeff posted some relevant details related to this on another thread:
Wikipedia has an article about depolarization. The idea is that there is a large impact on the neuron, but it doesn't actually fire. I am not a neuroscientist, though, so someone else may have a better explanation or resource than that.
To pull out what I see as some of the more relevant details for understanding the concept of "predictive state":
Once the stimuli have reached the cell body, the nerve must integrate the various stimuli before the nerve can respond. The stimuli that have traveled down the dendrites converge at the axon hillock, where they are summed to determine the neuronal response. If the sum of the stimuli reaches a certain voltage, known as the threshold potential, depolarization continues from the axon hillock down the axon.
This first point indicates that depolarization of the cell must reach some threshold level before it will transmit an action. Depolarization can happen without the neuron firing.
Next, from the linked article on Action Potential:
neurotransmitters then bind to receptors on the postsynaptic cell. This binding opens various types of ion channels. This opening has the further effect of changing the local permeability of the cell membrane and, thus, the membrane potential. If the binding increases the voltage (depolarizes the membrane), the synapse is excitatory. If, however, the binding decreases the voltage (hyperpolarizes the membrane), it is inhibitory.
I think understanding that hyperpolarization is inhibitory and depolarization is exitatory, and pairing that up with the idea that depolorization is not a boolean event, I think it is easy to understand a state in which a cell has been depolorized, but at a level which is below the threshold -- in this state it is "primed" to fire. This is what is referred to as "predictive state".