What is a neuropsychological test and what does it measure?

Depends. As noted there are many different tests and these are usually combined in a "battery" that attempt not only to measure the degree and severity of brain abnormalities, but also try to predict how individuals will function given the injuries, deficits, or degrees of decline. The tests are also used to track the progression of a disease, and plan rehabilitation treatments and programs.
Many tests. There are a variety of neuropsychological tests and each measures something different but all measure some aspect of brain functioning. They may be called for to assess memory or some aspect of brain function after trauma, stroke or some other head injury. It can also be called for when assessing adhd. Useful in helping clarify diagnoses and determine an area of the brain that may be affected.
Neuro. extensive. Neuropsychological tests measure memory, concentration, visual-spatial, problem solving, counting, and language skills. Examples of these types of tests include the Bender Visual-Motor Gestalt test, Wechsler Adult Intelligence Scale, Benton Serial Digit Learning Test, Hopkins Verbal Learning Test, California Verbal Learning Test, Knox Cube Test, and the Wechsler Memory Scale. Results are analyzed, taking into account the patient’s age and developmental stage. The neuropsychologist also studies emotional responses and other aspects of a patient’s mental state so treatment for depression or other mental conditions can be pursued.