Icelandic has one reflexive possessive pronoun, sinn. In this table I’ll include the regular possessive forms from Personal Pronouns and Possession, so you can easily compare and contrast. Notice that sinn is basically equivalent to the English own.

I’ve gone ahead and put word forms that are identical into little boxes. You'll notice that sinn is the same for every gender, and even in the plural.

Sinn inflects (changes) depending on what it is the person possesses, and the possession can sometimes have the definite article (the word the in English), depending on the kind of thing they possess and how formal or informal you want to sound.

As a side-note: there are other ways to indicate possession in Icelandic, notably with:

• the possessive pronouns minn and þinn, 
• the personal pronouns in the genitive case; and with 
• any noun in the genitive case.
  

If you’ve already mastered using minn, þinn, and the personal pronouns in the genitive (which you probably should if you’re reading this), the whole definite article thing shouldn’t be an issue for you; it works exactly the same. Instead, let’s use this article to focus on reflexivity. 

Inflection

Just to get this out of the way: sinn inflects exactly like minn and sinn, just with an s instead of m or þ. If you’ve already mastered those, sinn shouldn’t pose a problem.

Reflexivity

Sinn is a reflexive possessive pronoun. That means that it refers back to what you just mentioned, or more formally, it refers back to the subject.

Above, I mentioned that sinn is basically equivalent to own. However, English often omits that own, making things really ambiguous. Icelandic doesn’t hold with this sort of ambiguity. Here are some sentences that are ambiguous in English but perfectly clear in Icelandic.

• Jón fór út að ganga með hundinn sinn > Jón walked his (own) dog.
• Jón fór út að ganga með hundinn hans > Jón walked his dog (some other man’s dog).

• María kyssti kærasta sinn > María kissed her (own) boyfriend.
• María kyssti kærasta hennar > María kissed her boyfriend (some other woman’s boyfriend).

• Blær talaði við vin sinn > Blær talked to their (own) friend.
• Blær talaði við vin háns > Blær talked to their friend (some other person’s friend).

• Krakkarnir léku með leikföngin sín > The kids played with their (own) toys.
• Krakkarnir léku með leikföngin þeirra > The kids played with their toys (some other people’s toys). 

minn and þinn, okkar and ykkar

You may have noticed in the table at the start that I didn’t include the 1st and 2nd persons (I, and we; you and…*sigh*… y’all). That’s because they don’t use sinn for reflexive sentences; they use the same forms as for the regular possessive. Here’s the full table.

Check out The Possessive Pronouns minn and þinn and The Personal Pronouns and Possession if you’re not familiar with those already.

• Ég gleymdi afmælinu mínu > I forgot my birthday.
• Langar þig ekki í þína eigin köku? > Don’t you want your own cake?
• Við gleymum aldrei niðurlægingu okkar í skóla > We never forget our humiliation in school.
• Þið skuluð taka draslið ykkar og fara > Y’all should take your stuff and go.

Summary

Sinn inflects just like minn and þinn (which you should probably get pretty good at before you worry about sinn).

Sinn is reflexive, which means it refers back to the subject. Its English equivalent is (sort of) own, like her own, but English can often omit it. English is very ambiguous and weird.

The first and second persons (I, you, we, y’all) don’t use sinn. The regular possessive pronouns work reflexively, here.