The ragged edges round the side of your nails are called hangnails. They are caused when the dehydrated cuticle becomes attached to the nail and as the nail grows the cuticle stretches and eventually snaps.
To prevent hangnails you should gently massage your cuticles on a regular basis with a nourishing cuticle cream or a vegetable oil such as almond oil to keep them soft and pliable. This is best done after a bath or before going to bed to allow time to be absorbed. If they are very dry and stuck to the nail you might want to use a hoof stick to help lift the cuticle away from the nail plate.