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 the generic “his.” “Their” has long been used in this way in speech, and it is now acceptable in writing as well.