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。
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.
Each student determines their own pace in the yoga class.
每个学生决定他们自己在这个瑜珈班的学习速度。