As far as space goes, in 1=dim the minus sign (negative) is just a reverse of the positive direction. This finds application in problems like the calculation of Work done. Work is defined as
As long as the movement is along the line of force then a positive force in a positive direction will result in positive work done. However if the movement is against a positive force in the negative direction then there will be work given up. As a side note, itīs this feature that allows the Law of Conservation of Energy to be true.