In some situations, the comma (pause, in speech) will imply that there are other potentially contextually relevant countries / friends of mine, but the speaker wants to single out one in particular (Korea, Daniel).
In other contexts there are no credible alternative countries or friends being "ruled out" in favour of the contextually-relevant one - the speaker is simply indicating that Korea is a country, or that Daniel is a friend. Alternatively, that the relevant country's name is Korea or the relevant friend's name is Daniel. Only context determines which of those two aspects of the country:Korea or friend:Daniel relationship applies.
Formally speaking, the version with commas / pauses is called...
apposition - A relationship between two or more units especially noun phrases, such that the two units are normally grammatically parallel and have the same referent, e.g.
Our longest reigning monarch, Queen Victoria, reigned from 1837 to 1901
But quite where we draw the distinction between Albert married the Queen, Victoria in 1840 (which certainly looks like "apposition" to me) and "adjectival" additional information, such as Victoria married her cousin[,] Albert[,] in 1840 (where those optional commas have no effect on the meaning) is a matter for debate (if indeed the "answer" serves any useful purpose, which I doubt).