The purpose of trimming a cat's nails:
1. Prevent nails from growing too long and damaging the paw pads. If nails are not trimmed for a long time, they can easily grow abnormally, even growing into the cat's paw pads. This will cause the cat to feel pain when walking, and over time it can lead to inflammation and abscesses in the paw pads.
2. Prevent your cat's nails from breaking during play. If a cat's nails are too long, they can easily snag on the nails during play, running, and jumping, causing them to break and bleed profusely. 
3. Prevent cats from harming other people or animals. Cats' claws are too sharp, and they can easily scratch others accidentally when playing with humans or other cats. They can also easily cause serious injury to other animals during fights.
4. Prevent cats from damaging furniture. When a cat's nails grow too long, it will constantly scratch them, which will cause it to scratch furniture, sofas, etc., and it may also damage curtains, bed sheets, etc. while running and jumping.
5. Prevent excessively long nail lines. If a cat's nails are not trimmed for a long time, the nail line will grow longer and longer, eventually requiring nail trimming as a last resort, which is very painful for the cat.