“Justice sensitivity” is a character trait describing how readily and intensely one detects injustice, feels moral emotions in response (e.g., guilt, shame, anger), and is motivated to restore justice.
For this debate, you are “behind a veil of ignorance,” meaning you are engaging in a thought experiment as a hypothetical unborn individual who is perfectly rational, knows broad facts about society, and knows they could be born into any position around the world (but not which one).