Research has asked what changes in the brain when someone becomes conscious of a stimulus; in other words, what are the neural correlates of consciousness.
Neural workspace hypothesis: Different areas withing the brain seem highly specialized in their function. Each of these areas does its own job, and the activity in each area is highly transient: the neurons respond to the current inputs and then move on. We need to sustain the activity in these various systems, and we also need to integrate the activity of the different systems into a choerent whole. What makes this possible is attention, probably implemented biologically through top-down activation controlled by the prefrontal cortex. This activation can amplify the activity within specific neural systems, and it also can sustain that activity. Attention seems to link the activity of different neural systems, binding these into a single representation.
This large-scale integrtion of different neural processes is supported by "work space neurons", neurons that literally connect one area of the brain to another. The ingetration is selective, so it's certainly not the case that every bit of neuro activity gets linked to every other bit: various mechanisms create a competition among differnet brain processes, ant the "winner" is this competition is communicated to other brain areas. The information flow is limited but is also to some extent controllable, by virtue of what the person chooses to pay attention to. The integrated activity, made possible by the workspace neurons, literally provides the biological basis for consciousness. The workspace neurons themselves don't carry the content of consciousness. The content is presumably represented in the same neurons, the same processing modules, that analyzed the perceptual information in the first place.