A paring knife is a small, lightweight knife with a straight cutting edge. It's a real all-purpose knife, ideal for peeling and other small work. Often used to peel fruits or vegetables that are held in the hand.
A boning knife has a thin, flexible blade. Used to remove bones from cuts of meat. The thin blade allows to get into small spaces.
A santoku knife is an Asian style knife with a straight edge. It's an all-round knife for a variety of tasks. The wide blade allows for some typical activities like crushing garlic and scooping up the chopped ingredients on the blade.
With a carving knife it's simple to slice thin cuts of meat. Often used in combination with a carving fork to hold the roast.