"の" (no) can be thought of as a "general connective" in many ways just like "of" in English, "de" in the Romance languages, "von" and "van" in German and Dutch respectively, and "的" (de) in Mandarin Chinese.
Unlike English "of" however the items on the left and right of "の" (no) must be switched. This makes it even more like the English possessive apostrope:
Andrew の kuruma -> car of Andrew or Andrew's car.
Joining several nouns together differs between English and Japanese so often Japanese will have to add の between two nouns that English would just put next to each other. (And sometimes the opposite may be the case).
Even in English when you think about it there are lots of places we use "of" which don't really indicate possession but rather just part of our idiom for connecting nouns. The same happens with の in Japanese only it may seem more apparent not being your native language.