Take a look at this: http://web2.uvcs.uvic.ca/elc/studyzone/330/grammar/poss.htm
To hotrophanm. 11. 15.'20. Because it is the genitive form of she. Examples. She is here. I saw her. I have seen her. Her, as the object. And her, as a possessive pronoun: it is her book. This book is hers. Meaning that this book belongs to her. And also: these books are hers. Mine. Mine. Your. Yours. His. His. Her. Hers. She, is the owner of the car. It is her car. The car is hers. It is hers. Hers is here. (Meaning the car that belongs to her.) Our. Ours. Your. Yours. Their. Theirs. I hope that this way of answering your question was helpful.
Vietnamese is a monosyllabic language - the words are short and combine together to create meaning. Unlike English or German which combines syllables into long words. Cua co ay = belongs to her. Cua =belong to / owns etc. Co = feminine second person pronoun (ie 'you' when speaking to a woman). co ay = third person feminine pronoun, 'her / she'. Anh = second person masculine pronoun, 'you' when talking to a man older than you. Anh ay = third person masculine pronoun, 'he / him'. It's just a characteristic of the language - many Asian languages are like this. So 'Cua co ay' = belongs to her. But in English we can use a short form, 'hers'.