This is an idiom. This means that every person has two personalities but both the personalities are of importance. One of them is liked / disliked by some and the other side is also liked / disliked by some.
The proverb "Every coin has two sides" refers to human nature as the behaviour in a person changes in different situations. For example, a person may be too polite while talking with you but disrespects his inferiors. It also says that a person has two sides of reactions and language while in situations where he'd like to gain something.