The automatic chatter that goes on in the human mind which is, essentially, how we keep the Dream of the World intact.
Internal dialogue is everything from the lists we create to tell ourselves that a tree is a tree and a dog a mammal, to the inventories we run upon awakening each morning.
Internal dialogue, in short, is the language of the program, and one of the prerequisites to any serious spiritual journey is learning to stop that automatic self-programming so that we can hear the silence and access the deeper levels of the mind itself, including the state of gnosis.