A farm name is a kind of surname used in the Nordic countries, especially in Norway.
Farm names were usually added to the given name and the patronym and originally functioned as an address rather than as a surname.
When name laws were introduced in the 19th and early 20th century and hereditary surnames became mandatory, many people decided to keep their farm name as a surname.
In Denmark many people who use a secondary patronym chose to take a farm name as a middle name.
The meaning of the name Geir Sigmundsen Holmeseth is Geir (given name) 'son of Sigmund' (patronym) who lives on the farm Holmeseth (farm name).
Maybe Geir will marry a woman named Hilde (given name) Jonsdatter (patronym) Blomhaugen (farm name).
If they lived on the farm of Geir, their names would be:
Geir Sigmundsen Holmeseth and
Hilde Jonsdatter Holmeseth
If they lived on the farm of Hilde, their names would be:
Geir Sigmundsen Blomhaugen and
Hilde Jonsdatter Blomhaugen
And if they moved to another farm, their names could be:
Geir Sigmundsen Sandsgård and
Hilde Jonsdatter Sandsgård
Farm names usually consist of words related to nature. You can find a long list of farm name elements and their meanings here.