I think the claim is the an interface that revolves a bunch of different tools being applied to the image (e.g. the Lasso, Pencil, Paint, Eraser, etc. tools on the toolbar) is imitating paper. I don't know what the better alternative is.
It depends upon what you are starting with and what you are trying to accomplish. In times past, what you were doing the image editing on also mattered.
Programs like CorelDraw and Inkscape treat anything you draw as an object. If you want to draw a circle, it stores the parameters of the circle (e.g. position, radius, colour) in memory rather than a rasterized version of it. If you want to create a circle that looks like a sphere, you may draw a second circle inside the first circle to serve as the highlight, then connect the circles using a blend to create the gradient effect. If you don't like the position of the highlight, you move the second circle and the blend will be automatically adjusted. If you don't like the colour, you select each circle and adjust the colours. Of course, you don't have to limit yourself to colours. The circle could contain bitmap to end up with a textured sphere. The second circle doesn't have to be a circle either. It could be a crescent shape. I used to create some amazing looking alien planets using these techniques. You don't have to limit yourself to primitive shapes either. Graphics tablets digitize a number of different parameters for strokes. You could create a stroke with the pencil tool, then modify a parameter of that stroke so it looks like it was created by a calligraphy pen or a paint brush.
That description implies an intrinsic limitation: it's greatest utility is in image creation. You could store modifications to a pre-existing raster image in a similar way, but it is not quite as useful. For detailed images, it is also CPU and memory intensive. That's not a huge issue today, but it was a huge issue when people were initially developing the standard image processing techniques.
