their

Their is the possessive form of the personal pronoun they. It’s often considered a possessive pronoun, but it functions as a possessive adjective (also called a possessive determiner). That’s a lot of labels for such a common word, but they essentially mean this: their shows possession by functioning as an adjective and modifying a noun (it never functions as a noun itself). The same thing can be said about my (the possessive form of the pronoun I) and our (the possessive form of the pronoun we). (The forms theirs, mine, and ours stand alone as nouns and never accompany another noun as modifiers.)

In contrast, the word his can be used as both a possessive pronoun (as in That jacket is his) or a possessive adjective (as in That is his jacket). Possessive words like their commonly indicate possession or ownership, but they can also indicate things other than literal possession, like origin or other qualities (such as in phrases like their country).

Their is used along with third person pronouns (like they and them), which refer to anyone other than the person doing the addressing or the ones being addressed. Other third person possessive forms include his, her, hers, and theirs. In contrast, first person pronouns (like I, me, we, and us) refer to the speaker or writer themselves. First person possessive forms include my, mine, our, and ours. Second person pronouns (like you and yourself) are used to address the person being spoken to or reading. Possessive forms of these include your and yours.

Their can be used as both a plural possessive and a singular possessive.

Generic singular possession

They has a long history of being used to refer to an unspecified individual or to a person whose gender and other personal details are unknown or irrelevant, and their can also be used as a singular in this way, as in If a student is absent, they must bring in a note from their parent or guardian when they return to school. Sentences like this sometimes use constructions like his or her, but the use of their has become very common in such instances, with many people preferring their as less awkward and more inclusive.

Nonbinary gender expression

A use of their that has become more widespread is as a singular possessive form for those who use the singular, gender-inclusive personal pronoun they due to identifying as nonbinary or having a gender identity that exists between or beyond the spectrum of strictly male or female. Grammatically, their is used in the same way as the gender-specific terms like his and her, but it’s gender-neutral.

We don’t traditionally think of their as having synonyms, but there are several situations in which it can replace—or be replaced with—another term.

their own 

The phrase their own is sometimes used as a more emphatic way of saying their, as in I can’t believe they were betrayed by their own family members.

theirs

Sometimes you can reword what you’re saying to use theirs instead of their. For example, instead of saying This is their seat, you could say This seat is theirs. 

them

Sometimes, them is used where the word their could also be used, such as in sentences like this: Did you hear about them getting lost? Historically, it was considered more proper to use their before gerunds (e.g., getting in the preceding example), but using them is now more common and often sounds more natural.

Other possessives

Instead of saying things like This is her house and his house, we usually use the plural form their, as in This is their house. Sometimes, though, it makes more sense to separate who owns what by using separate possessive words. For example, instead of saying These are their vehicles, you could say This is his car and this is her truck. 

their vs. they’re vs. there

Be careful! Sometimes, their is used when it should be they’re or there—and vice versa. They’re is a contraction of they are. There is used to indicate where something is, among other things. Sometimes, they’re even used right next to each other, as in When they’re in there, they’re their own worst enemies.

Strictly speaking, their doesn’t have a definitive antonym in the same sense that short is the antonym of long. Of course, possession and association are often distinguished by using contrasting possessives, such as in statements like This is their responsibility—it’s not my responsibility. In this sense, all of the other possessive words could be considered the opposite of their, including my, her, his, and our.

On the other hand, one person’s possession of something does not mean that someone else can’t possess it as well.