Let's say we have 2 people, Søren and Mikkel. Søren owns a bird and Mikkel doesn't. I want to say that Søren hears his own bird, so I would say "Søren hører sin fugl" (Søren hears his (own) bird). Now I want to say that Mikkel heard Søren's bird, then I would say "Mikkel hører hans fugl" where "hans" refers to Søren.

This is because when the subject owns the object of a sentence, in Danish we use "sin" (or sit or sine depending on the gender of the object and if it's plural or not). If the subject doesn't own the object then we use the pronoun (here it's "Hans" because Mikkel is a male name). The "sin" pronoun only works for 3rd person singular things (so not for jeg, du, de or anything plural)