Hello Hela
It's a long phrase, but it simply means "a phrase that comes after the noun and acts as an adjective".
For instance, you might find a similar phrase as part of a subject:
1. Girls with short hair have cold ears.
Here, "with short hair" restricts the preceding noun: we can't omit it, since not all girls have cold ears.
Likewise, in
2. My best friend’s son has become a first violin in the orchestra of the Royal Opera House.
the underlined phrase restricts the preceding noun phrase "first violin": the news isn't that he's a first violin, but that he's a first violin with the ROH orchestra. (If a comma preceded "in the orchestra", we might say that the underlined phrase was non-restrictive.)
Is that any less murky?
MrP