Unlike the majority of the dwarves, who practice a form of ancestor worship, Burkel worships the Maker as a brother of the Chantry. He seeks to open a chantry in Orzammar and asks for the Warden's help to do so. This leads to the side-quest The Chant in the Deeps. He can be found near the entrance of Dust Town.
This section contains spoilers for: Dragon Age: Origins.
If the Warden chooses to help him, Shaper Czibor, in the Orzammar Shaperate, must be convinced since the Shaperate is responsible for such things. However, it is revealed in the epilogue that his endeavours to promote the Chantry were successful, which drew anger from some conservative quarters in dwarven society and the Assembly restricted the rights of Burkel's converts. While he was leading a peaceful protest against these restrictions, Burkel was killed when he was being arrested. News of this led to riots and the Divine considering leading a new Exalted March.
Note: There is a nug to be found behind him, needed for the quest A Lost Nug.