Rally Circuits are tracks that take place over snow or dirt. Rally Circuits can also have a mix of those and pavement. Tackling these tracks are different than the normal tracks, mainly because these tracks are more slick, thus causing you to drift, especially snow tracks. These kinds of tracks were introduced in GT2.
GT4 introduces tarmac rallies, which work the same way as normal street tracks but with an increased chance of crashing if you're not careful, thus penalizing you in the process.