I think you are talking about the particle の, but the character. (The character is the part of words, names, etc. )
There are various uses of の, but in the first step (for beginners), the text books teach it as "possession indicator".
Please take a look at these sites.
(How do you use (the particle) "no"? = 「の」(という助詞[じょし])はどのようにつかいますか。)
I hope it was helpful. If I understood wrong, please wait for other answers or please change the way of asking.