What is "the plane" in graph theory?

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I have learnt that a planar graph is a graph which can be drawn on the plane without any of its edges crossing. What exactly is "the plane"? In plane geometry, we define a plane to be a flat surface of two dimensions; however here the use of "the" suggests we have a particular instance of a plane in mind, not just any plane. Is there a certain specific type of plane which is meant here, other than the general plane from plane geometry?