I think when we talk about "unbounded lookahead," it means the lookahead can't be bounded by any constant. A common type of parser is called LR(1), meaning it can only lookahead by 1 character.[0]
The advantage of only looking ahead by a constant is that parsing can be done in linear time. For a backtracking parser, you have to look ahead by up to n characters each time, leading to a quadratic runtime in the worst case.