"Trust" in Moonbury reflects your standing within the community. Your current trust status is displayed in the upper left corner of the screen, denoted by a red thumbs down for low trust and a green thumbs up for high trust.
If your trust level is negative, characters will refrain from talking to you. Quests become inaccessible, and it's impossible to enhance your Friendship with any character during this period.
Trust is gained by successfully diagnosing and treating ill residents, whereas unsuccessful diagnoses and treatments lead to a decrease in trust.