Oscillation is everywhere-clock clicks, the light we see, the sound we hear, and even our daily life experiences are all oscillations. To me, the analogy of the ocean can still help to illustrate brain oscillation. Water and ice are both made of H2O but exist in two totally different states. The difference between liquid water and solid ice is determined by certain parameters, like temperature or pressure. When H2O is in the liquid state, like on the beach of Hawaii, crashing waves can be formed. However, on an ice cap in the Arctic, the ocean is covered by solid state H2O which only allows for small vibrations of the ice.

Now, the same brain consisting of the same cells can exist in different states, which are distinct like water and ice (both made of H2O). The basic building block of the brain is the neuron, which uses electrical and chemical signals to carry information. In each wave of slow-wave oscillation, neurons elevate their activities in a plateau form, termed the "UP" state. Just as water molecules influence nearby water with chemical forces, neurons can also change the activation level of other nearby neurons by specific connections called synapses. The waves can propagate across large regions of the brain by the collective action of many neurons through synapses. Following closely after the UP state, however, a silent phase follows, called the "DOWN" state. Each neuron only has about 20 millivolts (one thousandth of a volt) difference between UP and DOWN states. It may sound small, but because nearly all of the millions of neurons in brain take part in the oscillation between UP and DOWN states, the summation of the UP/DOWN states can be measured through the skull as EEG signals (with each state being very distinct from the other).

However, in REM sleep, all the neurons essentially stay in the same activation state, namely the UP state; one cannot find any large-scale propagation of activity or cycling between UP/DOWN states. There is still high frequency activity, usually in a local area, but this is drastically different from the global, synchronized slow-wave.

What state your brain is in largely depends on chemicals called "neurotransmitters" that are secreted by neurons. These neurotransmitters change the activity of neurons directly, and subsequently cause neurons to influence one another differently. A large amount of research has been published on this topic, so it would be difficult to provide a detailed background here. Instead I will provide an example of one informative study about the controlling of brain state, as I did for slow-wave oscillation and memory consolidation above.