Tapping the brakes after takeoff was a common practice in some aircraft (both light, and large), largely to reduce vibration from the wheels spinning in the gear wells. It also reduced gyroscopic forces on the wheel assembly and gear during retraction.
Some aircraft do not permit brake application after takeoff, and many aircraft use snubbers in the gear system which apply brake pressure during retraction to stop the wheels from turning. Dumping brake pressure once airborne helps prevent inadvertant application of brakes during the takeoff or during the landing, and prevents landing with brakes applied.