The Twin Flame basically means your Mirror Self.
This person is the other half of your soul. You love them deeply and have an intense relationship, with both really hot periods and then extremely cold spells. Fights are brutal because this person knows you so well.
They reflect your own strengths, weaknesses and vulnerabilities.
In some theories, the Twin Flame is someone you must outgrow, because you have to evolve into the New You every few decades or so.
The Twin Flame is a transformative relationship, one that changes you, completes you, hurts you, and then teaches you something when you finally end it.