The screw provides a means of converting a small force into a large one. Once in use, it allows pressure to be applied from different directions. These factors give the screw its relative strength as compared with a nail of the same size.
In the first case, the force applied to a screw is like the smaller force necessary to lift an object up an inclined plane rather than straight up. In a screw a form of inclined plane is provided by the spiral groove, called a thread, which cut round the shaft. By contrast the force applied to a nail can be compared with lifting an object straight up. If it were possible to unwind an inch-long screw, you would find that it was longer than an inch-long nail.
In the second case, the holding power of a screw or nail in a piece of wood depends on the pressure exerted on its shank by the wood fibres. A screw creates a far stronger grip because it presents a much greater surface area to the pressure of the wood.