During tasks that require continuous engagement, the mind alternates between mental states of focused attention and mind-wandering. Existing research has assessed the functional connectivity of intrinsic brain networks underlying the experience and training of these mental states using "static" approaches that assess connectivity across an entire task. To disentangle the different functional connectivity between brain regions that occur as the mind fluctuates between discrete brain states, we employed a dynamic functional connectivity approach that characterized brain activity using a sliding window. This approach identified distinct states of functional connectivity between regions of the executive control, salience, and default networks during a task requiring sustained attention to the sensations of breathing. The frequency of these distinct brain states demonstrated opposing correlations with dispositional mindfulness, suggesting a correspondence to the mental states of focused attention and mind-wandering. We then determined that an intervention emphasizing the cultivation of mindfulness increased the frequency of the state that had been associated with a greater propensity for focused attention, especially for those who improved most in dispositional mindfulness. These findings provide supporting evidence that mind-wandering involves the corecruitment of brain regions within the executive and default networks. More generally, this work illustrates how emerging neuroimaging methods may allow for the characterization of discrete brain states based on patterns of functional connectivity even when external indications of these states are difficult or impossible to measure.