Electric acupuncture uses a small electric current to particular needles.
Crocodile clips are placed on the ends of acupuncture needles once the needle has been inserted into the body. Then a small electric current is passed into the acupuncture needles to a tolerable level. It sounds uncomfortable and painful but isn't.
The electric current intensity starts off very low and is increased until the person can feel it and then slowly raised until a tolerable level is reached. It isn't painful but isn't relaxing as regular acupuncture as it is a strong form of stimulation.
A lot of research into acupuncture uses electric acupuncture as it's a stronger form of therapy and may achieve better results.
Personally, I only use it when there is numbness and nerve pain, which electric acupuncture is particularly good at treating. Otherwise, I find relaxing on the couch with regular acupuncture can be of more benefit than intense electrical acupuncture therapy.