Abdel Adrian does not actually appear in any of the Baldur's Gate games, as the actual protagonist is a fully customizable character. Rather, he is the protagonist in the novelizations of the games, which were written by Philip Athans and take a rather liberal approach to the actual plot of the games. The outline below describes the character as portrayed in these books.
Abdel was raised in the libraries of Candlekeep under Gorion's tutelage and guardianship. During this time, he was unaware of his lineage as a Bhaalspawn. He met and eventually befriended Imoen (despite constantly bullying her), a fellow orphan also cursed with the taint of Bhaal's blood. Upon coming of age, he left Candlekeep to pursue a living as a sellsword and find his place in the world.
He was eventually summoned back to Candlekeep by his old mentor Gorion to be warned about another Bhaalspawn's (Sarevok) plans. His quest began after Gorion was murdered by Sarevok's ambushing minions and he was accompanied by Gorion's friends Jaheira and Khalid. He eventually unraveled Sarevok's plans to drive Baldur's Gate and Amn into war, and discovered that he was a son of Bhaal, the God of Murder. His travels were paved with blood, as he continually slaughtered his foes, and ultimately, Sarevok.
Adrian's return to Candlekeep reunited him with Imoen but this joy was short-lived. His party was subsequently captured by Jon Irenicus, an elven mage interested in siphoning off Abdel's immense powers.
Baldur's Gate II: Shadows of Amn
Abdel wakes up in Irenicus' dungeon with his party and two other captives, Minsc and Yoshimo. They were able to escape after an attack by the Shadow Thieves, although Jaheira and Imoen were then captured by the Cowled Wizards. A mysterious woman, Bodhi, offered him help in locating his friends but this turned out to be a ploy to draw Abdel into Irenicus' hands again. Irenicus unlocked his latent Bhaalspawn powers and Slayer form, but Abdel barely escaped his captor. He put an end to Irenicus' plans to become powerful by stopping him from assimilating the elven Tree of Life's powers.
Baldur's Gate II: Throne of Bhaal
The final chapter in his life transpired when he successfully killed five other Bhaalspawn (The Five) who all aspired to become the next God of Murder. By doing so, he prevented Bhaal's resurrection.
Characterization in the Forgotten Realms novels
Abdel was a very well-built sellsword who had long dark hair, and was about seven feet tall. He generally evoked awe from onlookers, lust in women, and fear in his opponents. He was a skilled, brutal, and experienced combatant. He was a very impulsive fighter, shunning tactical planning and relying on his sheer strength to best his foes. His Bhaalspawn heritage lent him several abilities that allowed him to overcome his foes if he was ever outmatched in combat. These latent abilities became much more formidable after he realized his origins. Throughout the series, he discovered his ability to heal after serious injuries to be almost troll-like (breaking his spine and it healing within moments). This later extended to becoming impervious to normal weapons. The most drastic of his powers was his ability to transform into the murderous Slayer, the demon-like avatar of Bhaal.
Abdel was constantly plagued by the conflicting obligations to be a hero, and succumbing to the bloodlust that came with being a Bhaalspawn. He continually attempted to heed his loved ones' (Gorion and Jaheira) calls to lead a peaceful life, but still reveled in murder and was always forced to kill to make a living. The cognizance that what he was doing was wrong, coupled with his inability to turn over a new leaf constantly tormented him throughout his journeys.
Actual 'appearance' in a game
The closest thing to an appearance in the actual games is in Baldur's Gate: Tales of the Sword Coast. The expansion comes with a mission-pack save, containing a party led by a Neutral Good human male fighter named Abdel who has Kivan's portrait. The other members of the mission-pack party are Edwin, Viconia, Minsc, Jaheira, and Imoen.