In brief
border-spacing sets the distance between adjacent cell borders when border-collapse is separate. Two values allow different horizontal and vertical gaps.
Useful to know
border-spacing sets the distance between adjacent cell borders when border-collapse is separate. Two values allow different horizontal and vertical gaps. [1]
This is not the space between text and its border; padding controls that. If the setting has no effect, first check the border model, then identify which of the two distances you intend to change.
Sources
For further detail and to check the information: