It's mostly an issue when you lose traction in a corner and you have an angle between the steering wheels and the direction the power is applied.
FWD cars tend to pull the front end in the direction you want to go and if there is no traction you'll just under steer and slide sideways off the road. The back of the car is simply dragged along and power is ALWAYS applied in the direction the steering wheels. No net rotation on the car.
RWD though when you change the direction of the front of the car, instead of being dragged and following in line with the front, the powered rear wheels may continue to kick the rear out because the power is not applied in the same direction as the steering wheels. This makes RWD cars tail happy, and easier to rotate and spin out of control in poor traction conditions.
The end of the car that looses traction first has the least resistance to movement and leads the car, and naturally the part of the car that is powered will be more likely to break traction. In a FWD car the front wheels break loose first and the front of the car leads, while the rear still maintains traction with nothing else to cause otherwise. When RWD breaks traction, the front has more grip and the rear wants to swing around and lead, since it faces less resistance.
In icy conditions with RWD, people tend to loose traction with the front wheels first, trying to turn too fast, while the rear is still gripping. In response they panic and feed more throttle to the still gripping rear wheels (to try to "turn faster"?) which starts to push the back of the car momentarily before the added power also breaks the rear loose, and now the car is both sliding AND rotating.
In my RWD car in ideal conditions, I can blip the throttle on a turn and swing the rear around right where I want it. Brief throttle breaks traction for an instant, swings the rear around, and when throttle is let off, the tires grip again. But on ice, the static friction that would otherwise cause the tires to regain grip after you let off, is much lower and the car continues to slide rear end first under inertia.
It's easy to see if you play with a toy car on a table, or even your cordless mouse right now. If you pull the front end and make rapid changes in direction, handling is predictable and you don't "lose" the car. But push it from the rear while making a sudden change of direction on the front and you'll likely rotate the car 180 degrees. Also your pushing finger may have trouble staying on the car depending on how far and how fast it rotates, etc. because the orientation of the car is less predicable, directly reflecting real driving conditions.