As a dog groomer, nails are a pretty serious thing. When a dog's nails get too long, the dog can't stand and walk properly. The toes will have to be held improperly or twist to the sides, and it can cause pretty severe joint issues. The toes become bruised and sore. And, the nails- especially dew claws- can actually grow so long that they curl back to the paw pad and puncture the skin, causing bleeding, pain, infection, and worse.
With overgrown nails, it can be necessary to get them done at a vet's office so the dog can be sedated, have the open wounds and sores taken care of, and sometimes even have the quicks cauterized to shorten them.
Trimming overgrown nails is often painful because they're sore, stressful because of the pain and because the dog isn't used to having their feet handled, and sometimes still does not get them as short as they should be. The vein inside the nail, called the quick, grows longer as the outer nail grows longer. If the nail is kept fairly short, the quick doesn't have a chance to grow and can even recede. We can only trim up to the quick or we cause bleeding, pain, and potential nerve damage (if we cut far enough into the quick) so if the quick is longer than the nail itself should be, well, the nails will still be too long immediately after the occasional trimming. It takes very frequent trimming to achieve short enough nails at that point. Nail grinding can speed up the shortening process- the pressure and heat can make the quicks recede faster.
The appropriate nail length is much shorter than most people think it should be: the dog's nails should not touch the ground when it is standing relaxed, but should be able to touch the ground in some positions. You shouldn't hear a clicking noise on tile when your dog walks. If you can, it's time for a trim. If your dog holds its legs/feet/hips/elbows awkwardly, has difficulty getting traction, or seems to walk awkwardly, it could be due to its nails.
Also, play with your dog's feet at home, please. It's much easier, faster, safer and less stressful (for the dog and human!) when the dog knows it's okay for a human to handle its feet. Most dogs are not naturally okay with it; it takes training.