I may be simplifying this, but I think it's just a fancy schmancy way of referring to the electrical "circuits" found in the brain, in this case the cortex (overall, or more specifically motor, visual, etc., as the case may be). Connectomics tries to map the connections between neurons, mainly in the brain, building what is, in some sense, a circuit. For some sentences in context:
These results indicate a tight correlation between the effects of sensory drive and maturation on cortical neurons and provide a new set of cellular mechanisms engaged in the postnatal refinement of cortical circuits.
...spontaneous cortical activity provides a recurring template of functional cortical circuits within the developing cortex and could contribute to the maturation of integrative connections between sensory and motor cortices.