Easiest way to explain interpolation is:
Regular mode 60 Hz -> Frame A, Frame B, Frame C
Interpolated 120 HZ -> Frame A, Frame A+B, Frame B, Frame B+C, Frame C.
It basically sticks an extra frame based on the previous and the upcoming frame, any major difference (fast moving objects) are calculated and interpolated into the newly created frame, creating a more fluid motion.
You're still getting the source 1080p resolution, but now with an intermediate frame added in-between each original frame.
My personal preference is to have interpolation off as I think it makes the scene look too fluid, almost unrealistic, but its really personal preference.