That is not so easy to explain. You can control a stepper motor with a single chip (ULn2003A or L298N) for example but you will need to build in all the protection yourself. To control the chip you will probably need 5V and for the stepper 12V or even 24V. A shield does this for you. It will be restricted with the maximum current but you have more flexibilty.
At first I started with single chip control but realised that a shield was easier. Even better are the shields which plug into the Arduino directly. Most shields will contrrol two motors or even four at once. Hope this helps you a little.