A person's consciousness transforms when they become aware of themselves from a higher perspective. It's a natural and mechanistic process.
It's similar to the experience of waking up from a dream. Whilst dreaming, you're conscious and aware… but not aware that you're dreaming. It's only when you wake up, and become aware of yourself from a higher perspective, that you realise you were dreaming (and that you're now awake).
In a lucid dream, a person wakes up whilst their body remains asleep. They become aware of themselves from a higher perspective, but continue to dream.
For the lucid dreamer, it's not something they can explain easily to other characters in the dream. Nor is it a question of having to prove anything. And unless they've been actively preparing to lucid dream, suddenly waking up whilst still asleep can be frightening and hard to deal with.
Regardless, as a consequence of their higher perspective, a number of things happen to the lucid dreamer. Firstly, they know a higher reality awaits: when they die in the dream, they wake up somewhere else. Secondly, even if they can't remember their waking life, their entire understanding of who they are transforms. Thirdly, they're forced to live a double life; continuing to play out their dream character whilst secretly knowing their true reality, and identity, is something else entirely.
Self-realisation is like a lucid dream.