They/them/their is a third person singular (themself) and plural (themselves) pronoun. Some non-binary individuals request others use this set of pronouns when they refer to them in third person singular.
"They" and its inflections can also be used to indicate an indeterminate gender, i.e., when the speaker does not know the gender of whom they are referring to  and/or as a plural pronoun for the third person.
Singular "they" was used in Middle English of the 14th century by respected authors such as Jane Austen and William Shakespeare . However, around the 1800s in An English Grammar by W. M Baskerville, generic "he" is encouraged by matter of number agreement . Although, as language is ever-changing, in the second half of the 20th century, this trend reversed among feminist circles in favor of neutral pronouns and against a male dominated language.
Sometimes when hearing that an individual wishes to use "they/them/their" as pronouns, cis individuals will cisplain grammatical conventions they do not understand. Singular "they" has a long history of use in the English language and accepted use in modern grammatical conventions .
A common response is "they is at the store? That's not grammatically correct!" This response displays either ignorance of grammatical conventions about which they are asserting to have superior knowledge, or deliberate misunderstandings. When referring to a non-binary person who uses "they" pronouns, the correct structure is "they are at the store".
"They are at the store."
"That belongs to them."
"That is their book."
- What To Do (And Not Do) When Someone Asks for Different Gender Pronouns
- See the Wikipedia article on Singular they.
- Pronoun Etiquette, by Robot Hugs
- Huddleston, Rodney; Pullum, Geoffrey (2002). The Cambridge Grammar of the English Language. Cambridge; New York: Cambridge University Press. ISBN 0-521-43146-8.
- Baskervill, W.M.; Sewell, J.W. (1895). An English Grammar.
- Miller, Casey; Swift, Kate (1995) . Kate Mosse, ed. The Handbook of Non-Sexist Writing for Writers, Editors and Speakers (3rd British ed.). The Women's Press. ISBN 07043-44424.