Morghul was a dragon, apparently male, associated with Princess Jaehaera Targaryen.
Shortly after the birth of twins Jaehaerys and Jaehaera Targaryen in the year 123, two dragon eggs were placed in their cradles. Two dragons soon emerged and Morghul became associated with Jaehaera.
At the beginning of the war of succession known as the Dance of the Dragons in the year 129, Jaehaera Targaryen is already associated with Morghul, but the dragon is still too frail to be mounted. When Jaehaera is exfiltrated from King's Landing by her father's followers, Morghul remains in the capital.
During the sack of Fossedragon in 130, the Shepherd's lambs manage to break through the lower gates into Fossedragon. Bound by heavy chains and unable to fly, Morghul and the other dragons fight the mob with horns, claws and teeth, their breath turning the place into a fiery inferno.
According to the chronicles, Morghul succumbed to multiple spear blows in his eye from the Burning Knight, who was literally cooked in his plate armor by the dragon's flames.
His head and those of the other dragons that died that day are planted on poles inside the ruins of Fossedragon. Every night during the Three Kings Moon, the Shepherd appears near them to harangue the crowd with his apocalyptic preaching.
When Lord Borros Baratheon comes to arrest the preacher, the heads are in an advanced state of putrefaction. On the last day of the year 130, the Shepherd is tied to a post, surrounded by the heads of the five dead dragons, and King Aegon II Targaryen sets his body on fire himself.