The neurophysiological significance of negative functional connectivity

During a certain cognitive task in my fMRI experiment, a significant negative functional connectivity (r > 0.6) was observed between two brain regions. This result indicates that during the performance of this task, the activation of one brain region inhibits the activation of another.

But what does this imply?

What could be the possible reasons for this inhibition?

Is there an existing theory regarding inhibition between brain regions as a mechanism for certain cognitive functions?