They know how to use music, water, herbs and chemicals to aid in curing and helping others
They know every ailment and sickness as well as how to cure it
For minor wounds they can quicken the healing process and completely take the pain away, the more severe the wound the harder this is and the more energy it drains. They cannot bring someone back from the brink of death.
If a person is dying and the fates deem that death is imminent, a healing nymph can keep that person alive, but for every minute they do it drains them substantially. This could be useful if the person who is dying wishes to talk to someone or tell someone goodbye. The longer the nymph sustains their life past when they should have died, the more risk to their own life.
As they are nymphs they do not age, remaining eternally young.
They have a telepathic/empathetic connection with nature and other nymphs
They can cause someone to feel overwhelmingly sick for a short period, preventing them from attacking
They can cause someone to become paralysed for a short time, preventing them from attacking
More than likely, a healing nymph would be created or turned into one by Apollo or another god or goddess who's scope encompasses healing, medicine, etc.