A head shy horse is one that does not like having its head or ears touched. (Ear shy is a term used if the animal objects only to the ears being touched). Needless to say, this makes bridling a difficult endeavor.
Head shyness can be caused by a variety of factors. Hasty bridling is one of them (a lot of school horses end up head shy from poor bridling techniques applied by beginners). Another very head shy horse I know had a bout of ear mites from which she still hasn't recovered psychologically - the sudden development of head shyness in a previously happy horse can be a sign of the presence of these unpleasant and hard-to-treat parasites.