The Aldebaran serpent was a reptilian lifeform native to the Aldebaran system. It had three semi-transparent cobra-like heads extending from a brilliantly glowing sphere hovering above the ground, surrounded by lights.
In the final draft script, dated 25 September 1987, Q first appears as a "rapidly rotating, blindingly brilliant, diamond-blue light", and only later assumes the form of an Aldebaran serpent, which is described as "a writhing snake with snapping fangs", "an instant away from fanging [the bridge crew]".  In the finished episode, the scene is shortened and the two forms (the rotating light and the snake) are combined into one.
The authors of the novel The Chance Factor were keen to feature an Aldebaran serpent as one of the animals used in the story, but realized that the creature would not be suitable as a riding animal. Nonetheless, the cover artist depicted a three-headed animal, necessitating some last-minute changes to the manuscript. (Voyages of Imagination, p. 697)
In the Q Continuum miniseries, Q turns Picard into an Aldebaran serpent during their initial trip into the past, saying that it was one of his favorite forms before humanoids began to evolve; he claims he did it to create a sense of antiquity. Picard's mind can't handle three viewpoints at once, so Q reluctantly changes him back.
According to the RPG sourcebook Creatures, the Aldebaran serpent lives in the rivers and lagoons of the southern continent of Aldebaran III. It is 2-3 meters long and weighs 80kg. It has a four-lobed brain located in its thorax. All three heads have sensory organs and venomous fangs. Some primitive tribes on Aldebaran III worship Aldebaran serpents as gods.