I would say its fin rot, not 100% sure though. I would do a 30% or so water change and add some salt at a tablespoon per 5 gallons. This will hopefully cure it if it is in fact fin rot. You could also try treating it with fish antibiotics.
Helpful info on Fin Rot....
"Fin rot occurs when the fish is stressed for some reason. The most common cause is poor water quality. Overcrowding the tank, feeding outdated food or overfeeding, and moving or handling the fish can also cause stress leading to fin rot."
"Treatment should include a water change, and careful examination of the aquarium conditions. If there is food debris, vaccumm the gravel and take care to avoid overfeeding. Start dating your fish food, as it loses the vitamin content fairly quickly after it is opened. Feeding fish fresh, high quality food, in smaller quantities is far better than frequent large feedings of stale foods."
"Check the pH and water temperature of the water, and make sure it is appropriate for your fish. Incorrect pH is very stressful for fish, and can lead to disease. Low water temperatures, particularly in fish with long flowing fins, can trigger fin rot."
"If the root cause is corrected, antibiotics will usually cure the disease itself. Use a drug that is effective against gram negative organisms. Chloramphenical, Oxytetracycline, and Tetracycline, are good choices. Treat according to manufacturers instructions."
Prevention:
- Maintain good water quality
- Keep proper water parameters
- Feed fresh food in small amounts
