You don't mention how old your cat is - according to my vet this is quite a common issue with older cats. Their claws thicken and need to be watched with care because the thickened claws can be more brittle than normal claws (my vet calls them "old lady nails").
Most of my 18-year-old cat's front claws are like this. While they are quite blunt, they don't shed the way they should (which is why the thickening), so you have to stay on top of them or they will end up curling over into your cat's paw pads and causing her difficulty and pain when walking.
Claw injuries (where the cat has caught her claw in something and pulled too hard) can also do this, in which case if you keep the claws trimmed they can gradually return to normal.
You will need to be extra careful trimming the thickened claws. They split quite easily and can split to the quick (happened to me...). Also, extending the cat's claw for trimming can be painful if the thickening is too extensive.
I've found that the scissor-style trimmers with the very small profile (I can't link, sorry - I'm at work and the sites will be blocked - I'll try to get a link in once I'm home) are best, but you will need to replace them as soon as you start having difficulty cutting the claws. The small curve allows you to get the lower part of the trimmer between the cat's claw and pad, even for very thickened claws.
Edit: here's a link for the kind of clipper I use for my cat's old lady claws: http://www.chewy.com/cat/jw-pet-gripsoft-cat-nail-clipper/dp/40179
If your cat is showing signs of pain when you try to trim her claws, I'd recommend you see your vet. You might want to consider booking regular visits to keep her claws trimmed so there's no need to fear the thickened claws overgrowing into her pads.
If she balks at having you touch her paws, you can try to get her used to this by working her paws and extending the claws while you're petting her - give her lots of praise and love when you're doing this, so she associates having her feet manipulated with good things. Extra treats when you trim her claws will also help to get her used to the idea that this is going to happen and that it's not such a bad thing (I will say I've never had too much success with this, but I've heard others have - it depends on the cat).