Traditionally used as a plural possessive pronoun, "their" has come to be a shorthand for saying "his or her."
Before the women's rights movements in the U.S. it was considered acceptable to say "his" when the
gender of a person was unknown but women took offense to this and demanded that people say "his or her" instead. This idea was adopted for a while, and it was
common to see people writing shorthands such as "his/her," but people eventually grew tired of this and started saying "their" instead. It was not long before English professors and teachers became upset by the
new trend, and to this day you can still hear them scream when you use it in a
paper, but that's really
okay because it's their fault for making
us say "his or her" instead of "his."