Damaged toenails are very common, especially in active dogs.  Most nail injuries occur as a result of a nail catching or snagging on plant matter, carpet, or other material while the dog is running.

Damaged toenails are extremely painful at the moment of injury.  In many cases, pain will persist until the damaged portion of the nail is removed by a veterinarian.   However, the vast majority of dogs with injured nails make complete recoveries.

Read more here