Have a browse of Tidgney's driving school on YouTube when you get a chance:
Weight shifting in simple terms is controlling the weight of the car to avoid exceeding the grip of the tyres under load. It basically means keeping your inputs as smooth as you possibly can to avoid any violent weight shifts that you don't want. Short shifting is a good example as the slower acceleration will keep more of the weight on the front for steering and as you've probably found out, steering too sharply into a corner will overwhelm the outside tyre and understeer but by feeding the steering on for the corner, it will load up that tyre gradually as the car leans into it.
