Displacement maps can closely approximate the geometric detail of having 1 triangle per pixel. All the work for displacement maps happens on a per-pixel basis inside a fragment shader (in simple terms, a little program that runs for each pixel of a triangle). You can wrap this displacement map over a single, large triangle and get the visual appearance of a much denser mesh.
The alternative approach of subdividing the mesh is orders of magnitude less efficient because GPUs are _very_ bad at drawing tiny polygons. It's just how GPUs and the graphics pipelines are implemented. A 'tiny polygon' is determined from how many pixels it covers, as you start dropping below a couple dozen pixels per triangle you start hitting nasty performance cliffs inside the GPU because of the specific ways triangles are drawn. Displacement maps works around this problem because you're logically only drawing single big polygons but doing the work in a shader where the GPU is much more efficient.