"svůj" can get translated as - můj (my), tvůj (your sg), jeho (his, its), její (her), náš (our), váš (your pl), jejich (their)
You use "svůj" in a situation where personal pronoun and possessive pronoun match (ie. I - my; you sg - your sg; he - his; she - her; it - its; we - our; you pl - your pl; they - their). "I have my car. Já mám svoje auto.; You have my car. Ty máš moje auto.; etc." I can go on, but I guess you get the point.
There is one situation where you need to be careful, because 3rd person sg and plural (he-his, she-her, it-its, they-their) can be ambiguous in English.
He does not see a car of his parents. (In Czech this sentence gets translated as "On nevidí auto svých rodičů." -> meaning a car of his own parents; or "On nevidí auto jeho rodičů." -> meaning a car of parents of another guy).
Ungortunately, it is impossible to support incorrect English for several reasons (technical, too much work, some people do learn English here). This course is for native English speakers and people with high level of their English. I improved my English when doing other languages here. Do the same.