An esper rating is a representation of a person's psionic potential. Even Humans with the highest esper ratings do not actually have any psionic abilities, but such individuals can acquire them under the right circumstances.
In The Ur-Quan Masters, Commander Hayes mentions esper ratings at least twice in the game. One time is when the Kohr-ah are allowed to win the Doctrinal Conflict. He says that crew members with high esper ratings got a feeling tht something very wrong had happened. A second time he mentions it is when you bring in the Taalo Shield in for study. He claims that whenever you put a charge anywhere through the shield, all crewmen with high esper ratings get a bad headache, and "all psionic activity is flatlined."