Refers to the small one- or two-person sled used in the winter sport of luge, or the sport itself. The word is a direct loan from French.
from French
He rode a luge down the icy course.
I watched the luge event at the Winter Olympics.
He slid down the steep course on a luge.
I watched athletes sliding down on luges at the Winter Olympics.
Borrowed from French 'luge', originally a Swiss French dialect word for a small sled.