Skyhighfallguy,
The best way to explain it is to use the lift equation, L=Cl1/2PV^2S (sorry I can't use the actual mathmatical symbols). We say that heavy, clean and slow produce the greatest vortices.
To counteract weight, there needs to be lift, the heavier the aircraft the more lift required. So using the formula:
Assume an aircraft has full flaps, but reduces its airspeed from a nominal value of say 100KTs to 80KTs, to maintain the same amount of lift he needs to increase the Cl
Assume no flaps, so a reduced surface area to the first scenario, but he flies at 100KTs, he still needs to increase the Cl to maintain the same amount of lift
So adding these all in, if an aircraft has no flaps, and a low speed he needs an even further increased Cl to balance the equation. With that, we can then deduce why heavy, slow and clean is the worst configuration. Wing vortices increase in strength as the "deflection angle" increases ie. the angle of attack (which is the thing that changes the Cl of an aerofoil).
I hope this helps, but I'm sure there is someone here that can explain better