swój = possessive of the subject of the sentence.
That's it in a nutshell.
two examples for ryanb
When a man loves his wife, you should say
On kocha swoją żonę. If you say On kocha jego żonę, it means the man loves somebody else's wife
when a woman loves her husband, you should say,
Ona kocha swojego męża. If you say Ona kocha jej męża, it means she loves somebody else's husband.
Hopes this helps.