The Mysterious Meter is a scale used in Catherine and Catherine: Full Body which is affected over the duration of the story depending on the choices the player makes as Vincent. The meter affects Vincent's own internal thoughts and ideas during key points in the game and the game's own endings.
While the meter is shown throughout the game, what each side of the meter truly represents is not revealed until the very end of the game when Trisha discusses what the player truly desires. The meter is to said to measure Freedom (Red) and Order (Blue), rather than what one may initially assume is a simple Good and Evil scale.
As a result of the neutral endings of the game being commonly called the 'Freedom' endings, a common solution for players to avoid confusion is to swap the terms "Freedom" and "Order" with "Chaos" and "Law" respectively in reference to another game series made by Atlus with a similar scale, Shin Megami Tensei.
Catherine: Full Body
Not much is known about what changes will occur to the meter in Full Body. However, there have been images showing cracks in the meter itself along with the meter appearing broken and distorted, likely tied to the new possible branches and endings in the game.