Nothing much really, mostly to see that all your paperwork is in order (licence, medical, MR, etc...) occasionaly an airworthiness inspector will have a quick look over the aircraft. On one occasion, they weighed all my passengers, freight, etc and then I had to explain my load sheet in detail.
They may ask you a few questions about the type of operation that you are about to perform, if you are reasonably well prepared, a ramp check is certainly no big deal.