A pulley is really a kind of wheel, just as a screw is a kind of inclined plane. But pulleys are so important that people give them their own category. A pulley is a wheel with two raised edges so that a rope or a string will run along the wheel without coming off. It's often also called a block and tackle.
As with a screw, you can use a pulley in several different ways. You can use a pulley to make it easier to pull a rope, to change the direction of a force, or to get more mechanical advantage and lift something heavier than you can lift by yourself.
With a fixed pulley, the pulley is attached to a hook or a wall and doesn't move, like the clothesline pulley in the picture here. A fixed pulley doesn't give you any mechanical advantage, but it changes the direction of the force. For instance, you can pull down in order to lift something up, or you can pull the upper clothesline toward you in order to move the lower clothesline away from you.
With a movable pulley, you do have a mechanical advantage: you can pull with less force for a longer distance to get the same work done. This lets you lift things that would be too heavy for you without a pulley.