I would say that the most important part if grooming well. Some people will just run a brush over the top layer of fur and think that is enough. You really need to brush down to the skin over the whole body. Brushing from the skin up to the end if the fur works best and it has to be done in small patches at a time. Combing is good to check for knots or matting. The whole body needs to be brushed, that means the belly, back, neck, face, ears, tail, feet and anywhere there is fur. Depending on the rabbit, the belly and genital area can be shaved or clipped short to make grooming that area easier and to keep dirt, hay, poop etc out of the area.
People who show angoras and other wool breeds will use a blower instead of brushing. This keeps more wool on the rabbit (brushing can remove wool from the coat), blows out the dander and opens up the coat. Blowing doesn't take as long as brushing and can get better results.
Rabbits who are not groomed properly will develop matting over the whole body. This makes it hard from them to move around freely, groom themselves properly and stay healthy. I have had to totally shave rabbits who were totally matted and the fur can sometimes come off as one big piece like a pelt. Since rabbits has thin skin, there is risk of cutting the skin as it does become hard to separate the skin from the matt. Matting can also hide some skin conditions or other health problems. A rabbit could have a sore that can't be seen and gets worse and worse until there is a serious problem. Mites and other parasites could live in the skin and fur and could be a huge problem before they are noticed, if the coat was kept in good condition these could be seen and treated much sooner. Any lumps and bumps can be more easily detected during grooming as well.