Translation:A best friend is a person's best friend.
It's an open compound word if there's a space between them. (Example: ice cream)
It's a compound word because "best friend" has a specific meaning, she/he's (one of) your closest friend(s). It doesn't mean she/he is the 'best' in the sense that they're the best in a competition. You wouldn't say "she's my best friend because he's best in everything." :)
Admittedly whether or not a word is compounded or not, is debatable in English, because it's not as easy to distinguish between two words and a compound word. The line is sometimes blurry.
Compounding words is also much more common in Norwegian. 'rødmaling' is a compound word, but would 'red paint' be considered one? Probably not.
Old English used many compounds because separating them would require every word in the chain of meaning to be inflected. After English lost its inflections (especially on adjectives), there was less need for compounds. That has to be very weird for non-native speakers.
This is a really silly sentence, but to explain in a less grammatic way: I consider that you can have several "bestfriends", e.g. your bestfriend from school, your bestfriend from uni, and a sibling you're very close with. It's like a title you can bestow upon several people. Meanwhile, your best friend would be your very best friend. The one you rank over all other friends, like in English.
"Best friend" is not a open compound word any moreso than "best shoes" would be. To be a compound word the two words need to create meaning that is otherwise not apparent from the normal adjective/noun relationship. Although many people are a bit promiscuous in using the phrase, your "best friend" is literally the best friend you have. On the other hand, your "living room" is (hopefully) not alive.