The conjunction of his or her, his/her, or his & her. Only used in the context of unknown sex of subject of the sentence: Neutral, unbiased writing.
The customer can use hiser credit card when making a purchase.
A shortening of the phrase "his or her." Hiser can be used as a pronoun to refer to a person of unidentifiable sex, or when writing about a person of unknown gender.
See also: himmer, hersh
I was talking to Pat at the bar when hersh scratched hiser crotch. I'm still not sure if that was unladylike or perfectly natural male behavior.