Okay, I take it this is a long-haired cat. Possibly Persian? Persians are notorious for matting up. And that sounds like what is happening, the fur on your cat is matting up. You need to comb the cat frequently. And I say comb, not brush, because a comb will help prevent matting better.
To get rid of the mats, it's as theliq says. You may need to cut them. But you must be very, very careful not to cut the cat's skin!! And yes, these matts can be very uncomforable to the cat and can tear their skin.
If you're not sure what to do, do as someone suggested and take the cat to the vet for a shave.
I've had a couple of Persian cats, and they take constant maintenance or they matt up like this. One cat I had would matt up if you didn't comb him at least every other day!