From the perspective of English, の has several different meanings. It can indicate possession, like putting (A)’s on the end of a word. In Japanese, however, the meaning is a bit broader, and shows that (B) is an attribute/possession of (A).

• これは妹（いもうと）の車（くるま）です。
  This is my sister's car.
• 今日（きょう）の夜（よる）。
  Today’s night. (Not very natural in English, but ‘tonight’ is an attribute of ‘today’ in Japanese, so it works)

In the first sentence, we can see that の is showing ownership, however in the second sentence, it is simply showing a relationship between (A) and (B).
の is also often used in the same way as が, to highlight the subject of a statement.

• 私（わたし）が好（すき）きなお酒（さけ）はビールです。
  My preferred drink is beer. (Alcoholic drink)
• 私（わたし）の好（すき）きなお酒（さけ）はビールです。
  My preferred drink is beer. (Alcoholic drink)