온(溫) is a Korean family name (성姓).
In general, Korean family names are composed of one or more clans, or 본관(bongwan, 本貫). Quoting Wikipedia,
A Korean clan is a group of people that share the same paternal ancestor and is indicated by the combination of a bon-gwan and a family name (clan name).
Bon-gwan are used to distinguish different lineages that bear the same family name. For example, the Gyeongju Kim and the Gimhae Kim are considered different clans, even though they happen to share the same family name Kim. In this case, Gyeongju and Gimhae are the respective bon-gwan of these clans.
A clan is named after the origin of their ancestors or the clan founder. Sometimes, a clan branches out of another clan, sharing the family name but having a different clan name.
경주, 금구, and 청주 are all place names, from which different clans of the family name On(온) come from.
So your sentence means:
On(온) is a Korean family name. There are around ten clans, including Gyeongju(경주), Geumgu(금구), and 청주(Cheongju).