Is “their” singular or plural?
The possessive adjective “their” is technically plural. Thus, it is most frequently used to indicate possession by a plural noun (e.g., “Tony and Kyra brought their children on vacation”).
However, “their” is also acceptable as a replacement for the singular possessive adjectives “his” or “her” in several circumstances: when the gender of the possessor is unknown, when the possessor identifies as nonbinary, or when a general category of people is being referred to (e.g., “Each student should submit their own work”).
Using “their” as a singular possessive adjective is typically preferred to using the phrase “his or her” or using “his” in a general sense. “Their” has long been used in this way in speech, and it is now acceptable in writing as well.