Mahúr was one of Uglúk's Uruk-Hai that captured Merry and Pippin during the time when The Fellowship parted.
During the raid on Uglúk's troop, Mahúr ambushed the Rohirrim from the edge of Fangorn Forest with a group of Uruks. Mahúr's men were then either killed or driven off by the Rohirrim.
The character of Mahúr was not used in the film but was mentioned in the book.
"Still there's one thing the fine fellows don't know: Mahúr and his lads are in the forest, and they should turn up any time now". - Uglúk to his fellow Isengarders.
This information came from The Lord of the Rings, The Two Towers.