"I love my wife."
Translation:Я люблю свою жену.
The difference is, a native speaker will very rarely use "мою" in such sentence when you can you "свою" or nothing at all. English allows, for example, for multiple "he", "him", "his" in one sentence ("Tell him to call me back when he has talked to his sister"). In Russian that would sound extremely robotic.
"Свой" and "себя" are reflexive pronouns that refer back to the subject of the clause:
- Ты знаешь своего брата. = You know your brother.
- Я знаю свою мать. = I know my mother.
- Он знает свою мать. = He knows his mother.
- Я думаю, что он знает свою мать. = I think that he knows his mother.
- Он злится на себя ~ He is mad at himself
- Мы довольны собой. ~ We are proud of ourselves.
- Меня раздражает, что они так довольны собой. = I am annoyed that they are so proud of themselves
By the way, using reflexives might get tricky in cases when there is no canonical subject. Certain kinds of functional subjects also allow using reflexives to a degree:
- Ей не терпелось оказаться у себя дома в кровати, под тёплым одеялом. = She was impatient (=eager) to be back in bed at her home, under a warm duvet. → here, терпеться is an impersonal verb that uses an "experiencer" and a clause. Still, the Dative functional subject is, apparently, subjecty enough to use a reflexive here
свой, like most adjectives/determiners changes form based on the word it's describing, so своего is the masculine genitive singular (or accusative singular for animate nouns as is the case here), while свою is the feminine accusative singular. Note that these endings are exactly the same as for мой and твой.
жена is an object of любить, which wants its object to be Accusative. Such verbs are called transitive (they are assumed to "directly" act on some object), though this is just a term:). I mean, you can sometimes guess that a verb takes a direct object (eg., писать, читать, делать, слушать, видеть, готовить, покупать, брать), but sometimes a different language decides to take an approach different from that in English.
- the word Accusative itself, both in English and in Russian (винительный) is also just a calque from Latin/Greek—you probably noticed that it is not immediately clear why it is called that.
Basically, любить works same as the English verb "to love" (grammatically). At this stage what you need to understand is that as soon as you have a verb, a predicate word or a preposition "acting" on a noun, the cases a noun can take are limited to what these require.