What is KL-Divergence? Why Do I need it? How do I use it?

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I am currently studying KL Divergence. But It seems very confusing that I don't maybe understand why do I ever need it and what is that for? As I have been reading stuff about Mutual Information, it looks like it is about the amount of Entropy between two probability distributions, for example, P(A) and P(B|A), especially for the conditional probability situation. Can somebody give me a clear explanation about KL-Divergence?