Learn Icelandic: Ég sakna þess manns.

The verb sakna (to miss) requires the object that you are missing to be in the genitive case. Since you miss "that man," both the demonstrative pronoun þess (that) and the noun manns (man) must be in the genitive.

Wait, isn't þess the genitive of það (it)? How does it mean "that" here?

It is both! The demonstrative pronoun sá (that, masculine) and the personal pronoun það (it, neuter) share the exact same genitive singular form: þess. Here, because it is modifying the masculine noun manns, it is acting as the masculine demonstrative "that."

Could I use þessa instead of þess here?

No, because þessa is the genitive masculine form of þessi (this), not sá (that). If you said Ég sakna þessa manns, it would mean "I miss this man" rather than "I miss that man."

Does manns always show possession, like "man's" in English?

Not always. While the genitive case is often used to show possession in Icelandic, certain verbs like sakna simply force their object into the genitive case by rule. Here, manns is just the direct object you are missing, with no possession involved.