Point - This is the metal insert that you insert in the shaft. There are some that will go over the shaft. There are many different types of points and picking one will depending mainly on what you're going to be using the arrow for. Will you be hunting or just shooting at the range?
Shaft - This would be the body of the arrow. This peice is most commonly made of carbon or aluminium. However, you will occasionally see them made of wood or fiberglass. In my experience the carbon fiber arrows are the best for hunting.
Fletching - This part of the bow is either made of feathers plastic vanes. The main purpuse of the fletching is to cause strategic wind drag to give the arrow stability and accuracy. There are usually three feathers/plastic vanes. Two will be the same color (hen feather) and the other will be a different color to set it apart from the others (cock feather).
Nock - This is the peice at the back end of the arrow that connects to the string of the bow. There will be a nocking point that will hold the Nock in place.