The medical term used for sleeplessness is insomnia. Insomnia is a common sleep disorder characterized by difficulty falling asleep, staying asleep, or having poor quality sleep. It can result in daytime drowsiness, lack of energy, difficulty concentrating, and irritability.

Option 1, somnambulism, refers to sleepwalking, which is a different condition where a person is physically active during sleep.

Option 3, hallucination, refers to perceiving something that is not actually present. Hallucinations can occur in various sensory modalities and are not specific to sleeplessness.

Option 4, nyctinuria, is not a recognized medical term.

Therefore, option 2, insomnia, is the correct answer for the medical term used for sleeplessness.