Any spool has its optimum speed it can operate. So with a single spool , this speed is not the most optimum for each stage of the compressor and turbine , so by adding more spools more stages can operate closer to the optimum.
A triple spool willl have more stages operating at their optimum speed than with a twin spool and as a result can be more efficient, however there is a weight offset by having the extra spool and it also can make the engine a little more complicated.
I could get into blade tip speeds etc etc but thats the general idea.