In the SFM, a single frame is not a still image; it's 1/x of a second (x being the number of frames per second your project is working in, default being 24). This means that any object in motion in the frame is in a slightly different position at the end of the frame than it was at the beginning. That motion data is stored in your session.
Progressive refinement is a rendering technique that creates motion blur, depth of field, and soft shadows by blending together slightly different versions of a frame many times. The more versions that are blended together, the higher the quality, but the longer the movie takes to render.
Currently, the amount of samples you can utilize towards progressive refinement are as follows:
Depth of Field: 8, 16, 32, 64, 128, 256, 512, 1024
Motion Blur: 8, 16, 32, 64, 128, 256