The usage of pronouns is one more obstacle for foreigners in the way of learning the English language. The pronouns "Его" [yevo] and "Своего" [svaivo] means the same thing out of context - belonging of an object to a person. The meaning of these pronouns is similar, unless we don't know whom we are talking about. But when we place a preposition in a context, it determines the whole meaning of this sentence. That is the difficulty - grammatically both of these sentences are correct but meaning of one of them will change drastically.
For example, we want to say that on arrival a man named Vasiliy picks up his luggage which he has checked in before departure. We know and want to say that it is Vasiliy's luggage. Here are two options, one of which has semantic mistake made by many foreigners.
В аэропорту Василий получил свой чемодан - Vasiliy has claimed his own luggage at the airport.
В аэропорту Василий получил его чемодан - Vasiliy has claimed his luggage at the airport.
It's obvious to native speakers that we are talking about Vasiliy's luggage in the first example. But it is absolutely not obvious to a foreigner because the pronoun "Его" (His) is masculine and there is nobody except of Vasiliy in this sentence. Thus, a foreigner concludes that the pronoun "Его" can be only referred to Vasiliy so one can say that "Василий получил его чемодан". But it is the wrong option.
In fact, the system of Russian pronouns is so completed that even if we don't say anything about another subject (except of Vasiliy), it can be there "behind the scenes" - the pronoun "Его" indicates that.
To avoid making mistakes, you should practise a lot.
1. Each time when you need to use a possessive pronoun, you should ask the questions: "who is a subject?" (whom are we talking about) and "whose object is it?" (whom does this or that belong).
Using the abovementioned example about lugguage, we see that the subject is Vasiliy and the object is Vasiliy's luggage. If a subject and an object's owner are the same person, we should use the pronoun "свой" [svoy]. We confirm that the luggage belongs to Vasiliy only in this way. If we say "Василий получил его чемодан" (Vasiliy has claimed his luggage), it will mean that the luggage is somebody else's. Although, we don't know whose it is.
Here are some more examples:
Василий любит свою жену - Vasiliy loves his own wife.
Subject - Vasiliy, object - Vasiliy's wife.
Василий любит его жену - Vasiliy loves his wife.
Subject - Vasiliy, object - somebody's wife.
Мария выгуливает своего пса - Maria walks her own dog.
Subject - Maria, object - Maria's dog.
Мария выгуливает ее пса - Maria walks her dog..
Subject - Maria, object - somebody's dog.
2. You can use both pronouns in combinations with pronouns of 1 and 2 person singular and plural and also with a verb in the form of imperative: for example, "Мой" [moy] (my) and "Свой" [svoy] (own).
Я отдал свою машину в ремонт = Я отдал мою машину в ремонт - I sent my car to be mended.
Дай мне свой телефон = Дай мне твой телефон - Give me your phone.
Мы воспитываем своих детей = Мы воспитываем наших детей - We raise two kids.
Вы отлично демонстрируете свои знания = Вы отлично демонстрируете ваши знания - You greatly demonstrate your knowledge.
Attention! You can't use "Свой" in compound sentences, in the case when we use pronoun as an attribute.
Он счастлив, что своя книга нравится читателям.
Он счастлив, что его книга нравится читателям - He is happy that readers like his book.