This deity was often conceptualized as a man in his prime, much along the same lines of a Roman or Greek god. He was shown as a bearded man, most likely naked, holding a thunderbolt in one hand and a wheel in the other.
I was unable to find actual myths associated with Taranis, but I did find some background information on him that explains a few of his features. Apparently, the chariot wheel in Celtic mythology was associated with the sun-, sky-, or thunder-god. The wheel is representative of the wheel of the year, which had eight divisions, and of the eight festivals (known as Sabbats today).
Taranis is often paralleled with other deities, such as Thor, Jupiter, Zeus, Tarhun, Ambisagrus, and the Cyclopes Brontes. Brontes was also associated with the wheel, but the other deities do not necessarily carry the same association.
The name and function of Taranis was recorded by the Roman poet Lucan (39 AD- 65 AD). Lucan claimed in Pharsalia that Taranis was part of a sacred triad along with Esus and Toutatis, and was a god to whom human sacrificial offerings were made, apparently via drowning or burning. Whether those accounts are true or not are unknown, as Lucan was observing from the outside. Sacred triads of male figures are unusual, but not entirely unheard-of.
Light and Dark Sides
Based off the associations with some of the other gods, it is possible that Taranis was something of a justice-enforcer as well as the god of thunder. Zeus and Jupiter were both deities in charge of dispensing certain forms of justice, while Thor is a protective deity. While it is unknown if worship of Taranis involved those aspects of personality, it is a logical assumption that can be employed.
The idea of the sacred triad would take more research, but seeing as how that record comes from a Roman poet who, by all accounts, never actually visited Gaul or Briton but stayed in Italy all his short life. When considering the function and personality of Taranis, I would actually discard the assertion that he’s part of a sacred triad, as there is no real evidence that supports this for any of the three deities involved.
Since there is such a lack of material to clearly describe Taranis’ personality, I would say to simply treat him with respect and be mindful of the role which we do know he played: thunder-god, a mighty deity who rules the storms, and who is associated with the eight-spoke wheel.