If you have ever replaced a toilet with a smaller toilet, you may have some challenges. Particularly if your new toilet has a smaller footprint. That is to say that the toilet you are installing doesn't cover the area that your old toilet covered. If you've ever removed an old toilet, you know that the area under it can be mighty unsightly.
There is a decorative floor plate that you can install to make up this gap. In my opinion, they are not pretty, but they are functional. If your options are replacing the floor or installing a cover, the cover all of a sudden doesn't seem so bad.
There are covers that allow you to install them without removing the toilet, but many require that you do. It really isn't any different that installing a new toilet with a small step thrown it.
Once you have the old toilet removed, you can add adhesive caulking to the flange and push on the cover plate and attach it to the floor. Install a wax ring (get the type with the rubber throat built into it) and then install the new toilet like normal.
Once you are finished, the base of the toilet will look somewhat out of proportion to the new smaller toilet, but it is cheaper than replacing the floor.