I believe that's usually called MSAA, Multi-Sampled AntiAliasing. It generally does work very well for making a pretty image but it's also a lot of samples that'll be redundant. That's why there's some things like CSAA, FXAA that try to only do it on places where there's higher contrast or on edges where it'll be most notable.
SuperSampling or downsampling (there might be some nuanced differences between the two). AFAIK, MSAA works at the render resolution and you can have it in addition to downsampling, although at a very poor ratio of computation to reward.
