As the name suggests, the cuff for the upper arm model will be placed midway between your elbow and shoulder, while the wrist one will, well, hug the wrist. This makes it more convenient since fewer articles of clothing will need to be removed for taking a measurement. Furthermore, this can be used by overweight people whose excess tissue around the upper arm might otherwise affect accuracy.
While still fairly reliable, wrist models are less accurate than upper arm ones, and your body must follow a strict position for a true reading.