Answer
Spontaneous activity is any neural activity that is not driven by a stimulus or task. It occurs during quiet wakefulness, sleep, and under some forms of anesthesia. It also occurs in slice preparations as "slow oscillations" or "UP/DOWN states", which is my area of familiarity with it. The up-state and the down-state are two sub-threshold membrane potentials (e.g. -80mV and -50mV) that occur disproportionally often because the neuron's membrane potential spontaneously oscillates back and forth between them. These slow (~10 Hz, or "alpha"), regular, oscillations can be caused by intrinsic properties of single neurons, network dynamics, or both. Check out the answer to Question 59 for more details on functional roles for this rhythm.
Spontaneous activity arises from synaptic transmission. In slice, it arises from spontaneous vesicle release, either cortico-cortically or cortico-thalamically. This may be the mechanism under other conditions – anesthesia and quiet wakefulness – but that idea is controversial.
Though spontaneous activity in slice is generated, as far as we can see, randomly, its patterns are highly-structured and non-random. This apparent paradox is resolved when we consider that this random process is occurring in a system that is itself very structured: connectivity and internal neural dynamics tightly constrain the possible patterns of neural activity, no matter the source.
Refs
First, a theoretical approach to the origins of spontaneous activity, based on in vitro recordings and modeling:
- Orlandi et al., 2013. Noise focusing and the emergence of coherent activity in neuronal cultures.
The next two references provide empirical evidence that spontaneous events aren't 'random' in the simplest sense, and their abstracts and bibliographies are excellent resources:
- Cossart, Aronov, and Yuste, 2003. Attractor dynamics of network UP states in the neocortex.
- Luczak et al., 2010. Spontaneous events outline the realm of possible sensory responses in neocortical populations
Finally, this reference sort of straddles the above groups, observing avalanche structure in vivo and relating that to theories of neural networks "on the edge of chaos":
- Peterman, Plenz, et al., 2009. Spontaneous cortical activity in awake monkeys composed of neuronal avalanches.
Background information on UP/DOWN states and neural oscillations at rest:
- http://www.scholarpedia.org/article/Up_and_down_states
- http://en.wikipedia.org/wiki/Neural_oscillation
For cognitive folks, the notion of "quiet wakefulness", connects to resting state fMRI and the default-mode network:
- Greicius, M. D., Supekar, K., Menon, V., and Dougherty, R. F. (2009). Resting-State functional connectivity reflects structural connectivity in the default mode network. Cerebral Cortex, 19(1):72-78.