How does the Covariance Formula make sense logically and intuitionally?

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The covariance formula gives the linear relatinship between two variables and is an extension of Variance formula , given by E((X-X')(Y-Y')). Can somebody explain how the formula is able to capture the relationship between the two variables both in a logically and in an intuitional sense of how the math works, as i am finding it difficult to conceptualize it.