This is the 243rd most frequent Icelandic word.
jónsson
"Jónsson" is an Icelandic patronymic meaning "son of Jón."
Here, 'Jónsson' acts as a common Icelandic surname meaning 'son of Jón', following Icelandic patronymic naming conventions.
Jón Jónsson býr í Reykjavík.
Jón Jónsson lives in Reykjavik.
In this sentence, 'Jónsson' is used standalone as a reference to an individual, commonly understood and used in casual or familiar contexts.
Ég hitti Jónsson í gær.
I met Jónsson yesterday.
Here, 'Jónssonar' is the genitive case form of 'Jónsson', indicating possession, a typical grammatical structure in Icelandic to show ownership or relation.