We used to have horses and I learned early on the value of grooming them frequently. Not only is it good for their coat, you want to clean particles of dirt and other matter from a horse’s hair before saddling them to avoid rubbing sores on their back.
When you thoroughly groom a horse you have the opportunity to detect any potential health problems so you can nip them in the bud. Grooming is also a bonding experience. You and your horse begin to know and trust one another. This is true with any animal, 
including cats.
Frequently grooming your cat helps to alert you to a flea infestation, a sore spot, problems with the ears or claws. You’ll become aware of any unusual swelling, odor, or sudden weight gain or loss. Even a change in the texture and quality of the fur could be a red flag related to your cat’s health. And the process of grooming your cat can become a really nice bonding process.
Regular combing/brushing can also keep your cat from shedding all over your clothes and furniture. That’s a plus.
Your cat may resist certain part of your grooming routine, but go ahead with those things she loves and sneak in the other 
procedures during those times when she is most relaxed. I can generally trim the claws on one of Olivia’s paws during a lap session before she starts resisting. I do another paw the next time we cuddle.
As for whether to brush or comb and which type of grooming tools to use—I’ve found it depends on the cat. I’ve seen combs advertised as if they’re for all cats—wrong. There’s quite a variety of fur-types and you may have to experiment to find the grooming tools that work best for your cat. We have two sets of tools here because Olivia and Sophie have such different coats and tolerance level. Sophie begs for grooming with a fine-tooth comb. She loves it. Olivia, who has longer fur that tends to mat, isn’t a fan of the type of grooming she needs to minimize her matting and shedding. So we pick our battles with her and our opportunities and switch from the brushes that she likes to the tools that actually do the job. It’s a process.
