It's quick and easy - and it can save you and your cat some pain!
(Although it is possible for a neglected cat's nails to grow over, under, then up and through their paws. I know a cat who suffered this fate, she was rescued from a kitten mill in this condition. She survived and thrived with her new owner, although her gait was never quite the same. But assuming that your cat experiences a normal amount of mobility, this should not be a concern for the vast majority of cat owners.)
Your cat uses her nails, which keeps them worn down. The nail grows in stages, and each time it grows, it sheds off the outer cuticle. Imagine if your own fingernails shed themselves after they grew a little bit, so that you never really had to clip them. This is the situation with a cat's nails.
However, there are three very good reasons to trim your cat's nails: protecting yourself, and protecting your property, and protecting your cat from snagging a claw. I'm sure you have felt it when your darling begins to knead a little too firmly, and pokes you with those sharp claws! Plus, a trimmed claw will cause less damage to the carpeting and furniture. And finally, a claw which is long and sharp is more likely to get caught on blankets and upholstery. This is a situation which often leads to a torn claw, which is painful while it lasts.
If you get a kitten, start them early! I have found that the best nail clippers for cats are the ones that look like little scissors. They are easier to aim, and they are silent. Just the loud "ka-chunk" of the guillotine-style clippers seems to frighten many cats.
When you trim, you will just be taking the tip off the claw. Be sure not to get too close to the quick, that pink bit you can see inside the nail. Aside from the risk of accidentally trimming into the quick, if you trim too close to it, it can give your cat a pinch - the quick is sensitive!
Always be sure to get those "thumb claws," since they don't get as much wear as the others, they tend to be the sharpest. And when you hold your cat's paw, be sure not to squeeze the nubblet on the back of their wrists where those extra whiskers sprout - this is a sensitive area, and your cat won't appreciate having it grabbed!