When trimming a cat's nails, you only need to cut off the transparent part. Observe carefully in good lighting; you'll see the pinkish, fleshy part inside the nail at the base of the toe. This fleshy part contains living cells, blood vessels, and nerves. Cutting into this flesh will hurt the cat. Therefore, only the transparent part needs to be cut off. 
How to trim a cat's nails
To avoid being scratched, first have your cat lean against you, hold its paw, and gently squeeze out the nail. Make sure the nail clipper blades are perpendicular to the side of the nail, and cut from the thinner side. Cutting from the thicker side will split the nail. Choose nail clippers specifically designed for cats. Small scissor-style nail clippers are suitable for beginners or for trimming the nail tips. Large scissor-style nail clippers are suitable for older, harder nails. Guillotine-style nail clippers are suitable for long, thick nails, as they are strong and powerful; however, for overgrown nails, large nail clippers are more appropriate.