The Warhammer Army books include several different types of characters, be they Wizards or Heroes. However, we can easily imagine all kinds of wild individuals with different characteristic values from those given in the army lists. The characters described above are 'standard' types. They are typically representative of their race, and of the sort of Heroes and Wizards you can expect to find in a Warhammer army. Unique, named characters, those differing from the standard types, are referred to as 'special characters'.
Special characters are famous war leaders and mages, individuals renowned amongst their own kind and abhorred by their enemies. For example, they can be the mighty leaders of nations, such as the Emperor Karl Franz of the Empire; Goblin Warlords, such as Grom the Paunch of Misty Mountain; Malekith the Witch King of the Dark Elves, and many more besides. All of these special characters are quite different from the standard types. Some are better fighters than others, but some are better leaders, while many carry unique magical weapons or ride large monsters.
Numerous special characters are described in the Warhammer Armies books and other Warhammer supplements and, of course, players can make up their own if they wish. After all, who can resist the temptation to create a mighty leader of armies in their own image, to paint and perhaps even model him to suit their heroic vision, to name and invent a past for their character, and to deploy him in battle after battle!
The special characters models are normally equally exceptional, and players often field them in their army using the rules for a normal Hero or Lord character of their chosen army. This is perfectly fine, as long as you let your opponent know that the model is not the special character himself, but just a normal Lord or Hero that happens to look a lot like him!