The gray, and pinkish stains below the surface of the vinyl flooring found around the toilet by the home inspector indicates water damage. When there are stains around your toilet, there is probably a leak in the wax seal ring that seals the toilet to the plumbing flange at the floor. Continued leaking over a period of time will rot the flooring under your toilet and eventually leak into the areas below.
Try moving the toilet gently from side to side. Your toilet should not move. If it is loose, you will probably need to have a new wax ring installed.
Sometimes a quick fix can be completed by tightening the nuts at either side of the toilet at the floor. Usually these nuts are located under a small plastic cap. You will need to be very careful in tightenening these nuts. Your toilet is made of porcelain that can break if you over tighten, have uneven pressure, or poor support at the flange. Turn only a quarter turn at a time. When the toilet will no longer move, it is tight enough.