The sensor range was the range by which a sensor could detect someone or something.
In 2266, after Outpost 2 came within the sensor range of the USS Enterprise, the starship performed a sensor sweep of the area where the destroyed outpost had been located. (TOS: "Balance of Terror")
In 2267, the Enterprise picked up a Klingon scout ship at the edge of their sensor range. (TOS: "Friday's Child")
Later that year, as they attempted to locate an unidentified attacker, the Enterprise proved unable to find it in their sensor range. (TOS: "The Changeling")
In 2268, Commander Spock informed Captain James T. Kirk that Deep Space Station K-7 was within the sensor range of the Enterprise. (TOS: "The Trouble with Tribbles")
Later that year, the Enterprise detected a Tholian ship entering its sensor range. (TOS: "The Tholian Web")
In 3189, the speed by which the USS Discovery appeared in sensor range convinced the raider Wen that the starship had dilithium on board. (DIS: "People of Earth")