Taliesin was a Seer to the Great Kings in the time of the Old Religion. Though he apparently died around 300 years prior to the start of the series, he later appeared to Merlin and showed him to the Crystal Cave, which was said to have been the source of his powers of prophecy. He was aware of Merlin's destiny, and seemed to have foreseen their eventual meeting.
It is unknown how Taliesin was able to appear to Merlin. It's possible that he was a spirit, or an illusion created by the Cave itself. It's also possible that he never died at all, as he was shown to be able to use magic, or that he had the power to return from the dead at will.
Merlin met Taliesin when he and Arthur were ambushed by bandits in the Valley of the Fallen Kings. Though they managed to escape, Arthur was badly injured in the process and soon appeared to be nearing death.
After all of his attempts to heal Arthur with magic had failed, Merlin began to cry as he washed the prince's blood from his hands in a nearby stream. It was at this point that Taliesin appeared. He seemed concerned for Merlin, and asked him why he was so sad. When the warlock explained that Arthur was dying and he couldn't help him, Taliesin confidently replied, "Then do not waste your tears. For I can tell you that the time for him to die is not yet upon us." He then approached Arthur and used his magic to heal him, assuring Merlin that the prince would be fully recovered within hours.
While he was preparing to heal Arthur, Taliesin had introduced himself to Merlin (who he addressed as Emrys) and revealed that the moment of their meeting had been written for many years. Later, when the prince's condition appeared to be improving, Taliesin turned to Merlin and informed him that he wanted to show him something. He took the warlock to a nearby cave filled with magical crystals, which he identified as the Crystal Cave, the place where magic began.
Merlin soon discovered that he could see images in the crystals, which strongly reminded him of what he'd once seen in the Crystal of Neahtid. Taliesin explained that what he was seeing now was exactly the same, as the Crystal of Neahtid had been hewn from that very Cave. He then urged Merlin to look into the crystals, and assured him that much would be revealed if he did. Merlin initially refused, as the last time he'd looked into the future he'd seen terrible things, but Taliesin coaxed him into looking anyway. He told him that the future was hidden to all but a very few, and suggested that there was a reason that Merlin had been brought to the Cave at that moment in time. When the warlock asked what that reason was, Taliesin replied, "Only the crystals can tell you. They contain futures which are not yet born. The secrets they reveal, Emrys, are unique to you, and you alone." He then urged Merlin once more to look into the crystals, and told him to use what he saw for good.
Reluctantly, Merlin followed Taliesin's instructions and focused his attention on the crystals. He saw a number of images in their depths, including one of Morgana murdering Uther in his sleep. Horrified, he pulled away from the crystals and fell to his knees, holding his head as if in pain. Clearly in a state of shock, Merlin hoarsely demanded to know, "What was that?!" He received no answer, and when he looked up he discovered that he was talking to an empty cave. Taliesin had vanished (The Crystal Cave).
Taliesin appeared to possess a number of magical abilities. He was a Seer of some renown in the time of the Old Religion, and was among the few people able to see the future in the crystals of Crystal Cave, which was said to have been the source of his prophecies. He also had the ability to use magic, and at one point was seen using a healing spell more powerful than Merlin could cast to heal Arthur's injuries.
In addition (and possibly related) to his magical abilities, Taliesin was also able to speak with Merlin three hundred years after he was said to have died. How he was able to do so is unknown, but some possibilities are that he became a spirit after death; that he was an illusion created by the Cave itself to lure Merlin there; or that he had never truly died in the first place and had been living in or around the Cave for hundreds of years.
Interestingly, Taliesin's eyes were shown to turn orange when he used magic, as opposed to the usual gold.
In The Legend
In Arthurian Legend, Taliesin is occasionally named as a bard in the court of King Arthur. The idea dates back at least to the tale of Culhwch and Olwen (possibly a product of the 11th century), and was later elaborated on in modern British poetry such as Tennyson's Idylls of the King and Charles Williams's Taliessin Through Logres. He was often perceived as a legendary figure who existed in many different times, which explains how he was able to be present at Arthur's court when the historical Taliesin's career is known to have fallen in the latter half of the 6th century and King Arthur's death is often placed at around 539 A.D.
In Welsh Mythology
Historically, Taliesin was a renowned bard who is believed to have sung at the courts of at least three Brythonic kings, including King Urien of Rheged and his son Owain mab Urien. He was also a poet whose works may have survived in the Middle Welsh manuscript The Book of Taliesin.
In legend and medieval Welsh poetry, Taliesin is often referred to as Taliesin Ben Beirdd ("Taliesin, Chief of Bards") and was one of the five British poets of renown. According to the Hanes Taliesin, he was originally known as Gwion Bach ap Gwreang, a servant of the goddess Ceridwen who was made to stir the Cauldron of Inspiration for one year to allow the enchantress to complete her potion of inspiration. When the potion was finally complete, three drops sprang from the Cauldron and landed on Gwion's thumb. He instinctively put his thumb in his mouth to soothe his burns and gained the wisdom and knowledge that Ceridwen had intended for her son. Terrified of what the goddess would do to him, Gwion fled and eventually transformed into a piece of grain, which was consumed by Ceridwen.
When Ceridwen discovered that she was pregnant, she knew that it was Gwion and resolved to kill the child when he was born. However, when he was born he was so beautiful that she couldn't do it, and instead she sewed him inside a leather-skin bag and threw him into the sea. The child was eventually rescued by prince Elffin ap Gwyddno, who adopted him and gave him the name Taliesin. Later, when Taliesin was thirteen years of age, he correctly prophesied the manner and imminence of King Maelgwn Gwynedd's death.