Ona idzie na spacer ze SWOIM synem. = She's taking a walk with HER son.
Ona idzie na spacer z jej synem. = She's taking walk with her, i.e some other woman's, son.
Pan ma SWOJE gazety w biurze, nieprawda? = You have YOUR (own) newspapers in the office, isn't that so?
Ewa przyniósła SWOJĄ książkę.....= Eve brought HER book........ (as opposed to somebody else's!)
Ojciec idzie na spacer ze SWOIMI córkami. = The father is taking a walk with HIS daughters.
In Polish, "swój-" usually refers to one's own.
Widzę PANA gazetę. = I see your (singular polite!) paper. "SWOJĄ" would be wrong in this sentence, as the use of "your" is not reflexive here:-) In the above example, "Pan ma.....", the subject "pan" is referring to "his own", whereas in "Widzę pana.....", I'm an outsider looking inside, not the other way round.
A number of other languages have this idea of "someone's" (else's) vs. "someone's OWN"! Danish and Swedish as well as Russian make this distinction also.