Haywire chance is your character's spell critical chance. Haywire chance may affect any magical abilities. For instance, Vampirism is magic-based and might critically hit due to haywire. It is also possible to summon two monsters at once due to haywire.
Per patch 1.0.4, Vampirism and other non-spell abilities will no longer trigger haywire. It is currently bugged (1.0.3), and only triggers on non-spell abilities.