cocoanemo11,
The anatomy of the fingernail is actually quite complex.
The skin on the tip or end of the finger is continuous with the nail bed. The nail bed is a special type of soft tissue directly under the nail plate. The nail bed keep the nail plate "glued down" to the bone underneath. There is only a very small amount of tissue under the nail plate, but it is very vascular (has a lot of tiny blood vessels).
If you happen to cut the nail bed when you are trimming your nails, it will bleed very easily. The nail bed can be easily injured. This is why one gets a black nail after hitting it sharply (like with a hammer). When the nail bed is injured (torn) and it bleeds under the nail, it produces the typical subungual hematoma (black nail).
When a person has long nails, this allows some of the top layers of skin to accumulate just under the nail, at the tip of the finger. Then it becomes difficult to tell where the dead, top layer of skin ends and the nail bed begins. So, when you trim the nail plate, you nip the nail bed accidently. Some people call this cutting into the quick.
So, as nina586 stated, you might want to have a professional manicure. After that you could probably take care of it yourself. But, if you notice that the problem continues, have a professional take care of it.
Good luck.