Learn Icelandic: Hún skoðar skjáinn sinn. - She looks at her own monitor.

Sinn is a reflexive possessive pronoun. It is used because the subject of the sentence (Hún) is doing an action to her own monitor. If she were looking at another woman's monitor, we would use the invariable word hennar instead.

Why is the form sinn used here instead of sína or sitt?

The word sinn must match the gender, number, and case of the object being owned, not the owner. The word for monitor (skjár) is masculine, singular, and in the accusative case here, so the possessive pronoun takes the masculine accusative singular form sinn.

Why does skjáinn have the definite article -inn attached to it?

In English we just say "her monitor," but in Icelandic, when you use a possessive pronoun like sinn after the noun, the noun almost always takes the definite article. It literally translates to "the monitor her own."

Why is the word for monitor written as skjáinn rather than its dictionary form skjárinn?

The verb skoða (to look at or examine) takes an object in the accusative case. For the masculine noun skjár, the accusative form drops the "r" to become skjá, and when you add the accusative definite article -inn, you get skjáinn.