It means there is more than one reflection or account of that which is in question. What is usually in question is one persons reflection or account of a particular event. For example a couple who recently ending their relationship. Partner 1 says they ended due to X. But there are two sides to every coin so its possible that partner 2 could say that they ended because of Y. It is a phrase which advises you not to base your decision or opinion on one persons account or reflection. It advises you to listen to both sides accounts before you make your decision.
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It means that everything has two different ways that you can view it or think about it.
They work hand in hand to promote stability
Two Sides to Every Story was created in 1976.
Every polygon has two of its sides intersect.
As a coin has two sides, the odds are always 50-50.
joe hendy