What are special spells?
http://nethackwiki.com/wiki/Spellcasting
This chance of failure is affected by intelligence (or wisdom), experience level, skill level, innate magical ability of the role, armour: especially metal but also shields and robes, whether it is an emergency spell or your special spell.
A special spell has a higher rate of successful casting. Each role has one special spell. These are listed in this table.