The Default Mode Network (DMN) is a large-scale* brain area which was discovered during 'real-time' brain-scan experiments in the late 1990s.
The DMN was seen to decrease its activity during attention-demanding tasks, and then resume activity once the task was over.
Experiments in the early 2000s showed that the brain's energy consumption is increased by less than 5% while performing such attention-demanding tasks. - suggesting that the DMN is probably also performing highly complex operations. But a full description of those functions is currently lacking.
It's speculated that it may be involved in a large variety of different tasks - including 'mind wandering' and 'daydreaming' - and has even been called "the neurological basis for the self" (see Wikipedia).
For extensive details of the discovery of the DMN, and current views on its possible functions, see :
Annual Review of Neuroscience 38:433–47
A frequently asked question, which has an incomplete answer at this time, is, “What is the function of the default mode network?”
* Note: The DMN is not a single isolated brain area, but is a distributed network across the brain, linking the medial prefrontal cortex, the posterior cingulate cortex/precuneus and the angular gyrus, amongst others (see Wikipedia for details).