SAT: Separating Axis Theorem

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Does anyone here care to explain to me how exactly you would use it. I'm looking for a very simple real world example.

How can I use it to calculate the overlap of two convex polys, which are made up of an array of x and y coords.

The only thing I've ever been able to understand is AABB collision. So I might be a lost cause. Boy, do I wish I had a brain sometimes.