"Adaptive Supersampling" may refer to a lot of different techniques but generally it means a form of Anti-Aliasing where pixels are shaded1 a variable amount. It detects pixels that contain triangle edges and shades these pixels at a higher rate than not-edge pixels.
It is generally faster than pure Supersampling, as it avoids having to shade "nomal" non-edge pixels multiple times. For scenes with frequent depth discontinuities (thin bars, cables, antennas, grass) large parts of the image may get Supersampled which hurts performance.
Although Adaptive Supersampling is slower than Multisampling, it may provide better quality as it can mitigate specular edge artifacts2 to some degree.
Adaptive Supersampling is not generally implemented in major games because it requires rasterizing the scene with a multisampled rendertarget. Such rendertargets may become a substantial graphics memory bandwidth bottleneck as most major game engines use deferred shading3.
1 "Shading" refers to the process (implemented in a shader) of calculating the color of a pixel, how much light it "reflects" into the camera, taking lights, shadows, complex materials, etc into account and is therefore quite expensive and should be done as few times as possible per frame.
2 Specular Edge Artifacts: https://www.youtube.com/watch?v=VWRfLhOY2AA
3 Deferred Shading: https://learnopengl.com/#!Advanced-Lighting/Deferred-Shading