What does "hypermetabolic" mean on the report of a pet scan?

Takes up tracer. Pet scans work by imaging a tracer that is a sugar analogue. Since tissue/cells that are more "metabolically active" take up more glucose tracer, we refer to that as "hypermetabolic". Diagnostically, this can mean a number of things and depends on the context. Inflammatory cells and malignant cells (cancer) are typically hypermetabolic. One would have to look at the context and medical history.
Consuming more. Hypermetabolic means to be metabolizing (using, consuming) more. Most clinical pet/ct scans use f-18 FDG as the radiopharmaceutical injected into the patient. Fdg is an analog for glucose, so it images glucose metabolism. High glucose metabolism is seen in many conditions, including tumors (benign and malignant), infection (acute and chronic) inflammation and after surgery.
Over-active. A pet scan measures the metabolism of glucose. Areas that are overactive are called hypermetabolic.