ROPs are a big part of video cards. If you look at for example the GTX 760 vs the 660 Ti. They use the exact same architecture, but the 760 is able to achieve better performance despite having less CUDA cores due to ROPs. The main area where more CUDA cores can matter is in compute heavy scenarios.
As far as the function is concerned, here is a quote from a website known as GPUReview:
Raster Operators (ROPs) handle several chores near the end of the of the pixel pipeline. ROPs handle anti-aliasing, Z and color compression, and the actual writing of the pixel to the output buffer.
Recently nVidia has been reducing the number of ROPs on their graphics cards as shading power gets more and more important. For example, the 6600GT had 8 fragment pipelines, but only 4 ROPs. However, in just about any modern game, far more than 1 cycle is spent shading each pixel. Thus, cards with the same number of ROPs as fragment pipelines would end up with ROPs sitting idle waiting for input.
The move towards fewer ROPs than fragment pipelines is a way gpu designers eliminate unneeded complexity from their chips without sacrificing performance. And less complexity means higher speeds and better yields will be attainable.