Generally speaking, Wizards dislike armour. Its stifling bulk creates a deadening aura about the Wizard's physical body that blinds their Mage sight and makes it all but impossible for them to manipulate the Winds of Magic.
To represent this, a Wizard cannot wear armour or carry a shield. Should a Wizard ever do so, they are unable to make any Casting or Dispel rolls. This penalty applies to all armour and shields, magical or otherwise, but does not include barding (which is worn not by the Wizard, but by their mount).
Note, however, that there are some exceptions. Certain special rules, such as 'Chaos Armour' (found in the Warriors of Chaos army list), make a Wizard exempt from this penalty. Similarly, some suits of magical armour are crafted in such a way as to be exempt from this penalty.