Auberon first made his appearance in the comic book universe in The Sandman #19, and like his wife Titania, it is made clear that Morpheus made a pact with William Shakespeare. The details of the pact as to what Shakespeare had to do to fulfill his part of the pact are unknown. But it's believed that in exchange for the play "A Midsummer Night's Dream" Shakespeare took his troupe into the realms of the Faerie where they gave a live performance of the play for Titania and Auberon.
As in the play, there are several things that hit home with Auberon. He is indeed married to Titania.... and as the play suggests they have a very tenuous marriage. Made so by their not so infrequent trysts with mortals and other magical beings while still maintaining marriage to each other. But no mater what they always fall back on their love for one another.
Auberon usually appears as a fair blue skinned elf like faerie wearing Elizabethan period garments and sporting a pair of horns atop his head. This just could be because he's the King or it could have something to do with the artists wishing to show that Titania had made him a cuckold.
At any rate, Titania and Auberon rule the Twilight Realms of the Faerie. A realm that's home to many forms of fay and is subject to periodic changes of landscape due to their connection to the realm of myth and dreams.
For more on the tale of how Auberon became king, see "The Book of Faerie: Auberon's Tale"
Auberon was born into the Faerie royal family, its only member with a direct line of succession to the throne if the current King Magnus was to die. To protect him from possible assassination and Court intrigues, Auberon's cousin Dymphna and the brownie nursemaid Bridie too him to a far-flung corner of Faerie to raise him, where they used powerful wards and spells to protect him from any harm. However, Auberon couldn't be protected forever: when King Magnus died, an old admirer of Dymphna called Lord Obrey of Windan came to the child's house to take him back to the Court and the Throne.
As a boy-king, Auberon relied greatly on the counsel of Lord Obrey to secure the throne - who fortunately was extremely loyal. Auberon's belief in the righteousness of his claim led him to be too trusting of his subjects: he faced his rebel cousin Duke Hounnor of Grimwar alone on the field of battle and expected his surrender, not even considering that the Duke might take the opportunity to kill his rival for the throne; he took the Amadan's advice to reward Obrey's loyalty only with the thanks of a grateful king, something which drove a wedge between the two that was never repaired. Auberon was considered too naive to perform some of the grimmer duties of a king even by his supporters - when Duke Hounnor did honorably surrender to Auberon, it was Obrey who had him killed against the boy-king's instructions to pardon him - and it was on these grounds that Lord Obrey decided, after prompting from the Amadan, that the boy should be killed and that he should take the throne for the good of the kingdom. Fortunately, Auberon was aware of the dangerous position he was in, and slipped away before any harm came to him ostensibly to find his missing sister. His final note to his subjects appointed Lord Obrey as Regent, to rule in his stead until he returned.
Auberon searched for many years, engaging in a romantic relationship with an elf-lord's daughter, but when he returned to reclaim his throne, Obrey refused to stand aside and the realm was again split by war. Auberon defeated his regent in battle, and to reunite the war-ravaged kingdom married Obrey's widow and attempted to produce an heir with her. However, his new queen Lady Titania- felt aggrieved at exchanging a doting husband for one who appeared to see her as nothing more than a political pawn, and began a long series of affairs shortly after the wedding. Titania engaged in many such affairs throughout their marriage - even one of his lesser subjects was able to comment on how fitting it was that Auberon wore horns - but all the same, Auberon grew to love her in the face of her cold spite: he disguised himself as a maid named Selwyn so that he could spend time with (and eventually bed) his wife, and when he was trapped in a fantasy of his own making its main feature was that Titania repented her adulterous ways. Despite this, Titania frequently assumed that Auberon was being unfaithful with any woman who was in his presence.
Auberon remained blissfully unaware of Titania's first betrayal with a human falconer called Tamlin, and even when she fell pregnant he thought the child to be his. He sent for his own nursemaid Bridie to look after the expectant mother, who plotted with Titania to convince Auberon that the child was stillborn when it was born fully human: Bridie took the baby to the Mundane World (where it possibly grew into Timothy Hunter, leaving Auberon distraught at the idea he might have somehow caused his child's death by insisting on bringing in the brownie midwife. Auberon discovered the truth when Tim was a teenager, overhearing him refer to Titania as "mother", although he dismissed the idea by stating that Tim had no Faerie blood in him.
Auberon's years ruling an unchanging but feckless kingdom weighed heavy on him, and suffering from ennui he went walking in the Mundane World. Whilst there, he met a young woman named Gwendolyn who convinced him to try a magical device guaranteed to lift his spirits: instead, it stole his soul and left him a mute slave in an army of similarly tricked down-and-outs. When an accident left his fellow captives drowned, Gwen regretted her actions and attempted to save Auberon: as he didn't breathe air, he didn't drown but Gwen needed to help of Tim Hunter to free Auberon's soul and return it to his body. The experience deeply affected Auberon, and he swore to dedicate himself dilligently to his duties and responsibilities in the future.
True to his word, Auberon became a truly responsible ruler of his people, and even those who visited his realm: when Molly was brought to Faerie by the Amadan, Auberon ensured that she had food from Earth, and when the girl was tricked into eating faerie food by Titania, Auberon took it upon himself to find a way of lifting the curse - risking his own safety to try and track down the mystical gemstone Twilight.