Monologuing means speaking by yourself in the target language — narrating your day, describing what you see, reacting to something, or just talking about whatever comes to mind. No conversation partner needed.
Monologuing lets you practice word retrieval and sentence construction without the pressure of a listener. You can pause, restart, and try different phrasings without social awkwardness. It's the speaking equivalent of freewriting.
It's also always available. You don't need to schedule a partner, pay for a tutor, or have internet access. You can monologue while walking, cooking, driving, or any time you're alone. Or when you're with people, I guess... But that'd be a little weird.
Monologuing is introduced in Phase 4A and remains useful throughout all later phases.