It's a possessive pronoun that refers back to the subject of the sentence. Here, it's "Я", so it translates to "My".
If it was "Он", it would translate to "His". "Она" = "Her", etc.
Thank you for the explanation, although no matter what I cannot seem to get a good "feel" for the word, I am always thinking it means "his/her," possibly from influence of being a Spanish speaker, and thinking: su.
Своя рубашка - ближе к телу - Your own shirt is closer to your body (more important to you). 'Shirt' works like a parameter (template) here. What's belong to you is more important to you.
This word does not exist in English, but it's a handy one: it means "belonging/relating to the subject". If I talk about my stuff, this word would mean "my"; if the subject of the sentence is you, the same word would mean "your"; if the subject is someone else, the meaning would be "his" or "her".
You could use «мою» Instead of «свою» (the two should be conjugated the same way), but somehow «свою» sounds more natural to me.
Why is it «мою» (and «свою» for that matter)? Shouldn't it agree with «дочь», which is feminine?
Feminine nouns that end in a soft sign in nominative have the same ending in accusative. The adjective will always change into accusative as well.
In the accusative, masculine and neuter nouns that are inanimate keep the nominative ending, but the adjectives keep the nominative ending as well.
Sure, but that's how adjectives and posessive pronouns conjugate with feminine nouns in the accusative case. The noun itself looks the same as nominative, but not its adjective!
мою/свою agree in gender with the subject, but the adjectival ending declines in the accusative because they are the direct object of the verb люблю. Conjugation is for verbs, declension is the term used for cases.
Винительный падеж (Кого, чего) - свою дочь. It isn't just about male/female business, there are all these forms...
Agreement means have the same case/gender, etc, not necessarily the same suffix on the word.
"Любить"="to love" when you talk about people (like here).
At the same time "любить"="to like" when you talk about inanimate things/objects: Я люблю молоко = I like milk. English "to love" in reference to inanimate things is much stronger than Russian "любить" and better corresponds to something like "обожать".