Their is the third person plural possessive determiner. their 是第三人称复数所有格限定词。
1
[DET-POSS 所有格限定词]他们的；她们的；它们的 You use
their to indicate that something belongs or relates to the group of people, animals, or things that you are talking about.
Janis and Kurt have announced their engagement...
贾尼斯和库尔特已宣布订婚。
Horses were poking their heads over their stall doors.
马儿们从马厩门上探出头来。
...as the trees shed their leaves and the year begins to die.
随着树叶凋落，一年将逝
2
[DET-POSS 所有格限定词](代替 his or her，而不指明是男是女；有人认为这种用法不对) You use
their instead of 'his or her' to indicate that something belongs or relates to a person without saying whether that person is a man or a woman. Some people think this use is incorrect.
Every member will receive their own 'Welcome to Labour' brochure.
每个党员都将收到一本名为《欢迎加入工党》的小册子。
But anyone looking for income from their investments is in a much worse state.
但是，那些指望靠投资获取收入的人境况更为糟糕。
Usage Note :
Take care not to confuse their and there.
注意不要混淆 their 和 there。