I know it is been a while since this was asked, just want to contribute a little:
As you are a private pilot you probably have flown some little airplanes like a Cessna or a Piper and so on. As you know, the speed range of those planes goes from about 44 kt to 160 kt (Vso and Vne for a PA 28). So, in general your speed range is about 120 kt. A airbus has a never exceed speed of 0.9 Mach, which is (at FL350, ISA conditions) about 520 kt, and a stall speed of 112 kt. There is a 400 kt difference there! As you have surely noticed when flying, ruder corrections in cruise (fast) flights need to be much less extensive then on approach (slow flight). This is because there is less air flowing over the wing in a certain amount of time, therefore less lift is created. And if you lower an aileron to create more lift on one side, the lift created by that aileron is less then when you are flying fast. Therefore the force acting on the plane which would roll it is not as big, more extensive controls are needed!
To get back to the Airbus: The ailerons are designed to be used in fast flight, not so much for slow flight. As the wingspan on a Airbus is about 4 times the one of a PA28, the arm that a aileron has is higher on the airbus. Thus it does not have to create as much lift force to have the same effect(relatively!). Therefore it is not designed to create that much lift when it is being put down. Now as you get into slow flight, the lift created is less then in fast flight, and as moment = arm * force, and the force is reduced much, the moment is reduces, thus the effectiveness of the aileron is decreased.
Now the spoilers don't go down, they go up only when the aileron on the same wing would go up. Looking at a wing you will notice that the cord line changes when moving away from the airplane: The closer you get to the fuselage, the higher the angle is (You can see that on a prop especially!!). This again has to do with the arm, the wing can not carry as much load on the far end.
Therefore in slow flight, the spoilers are lifted. As you see in the video by DeltaLima, you can actually see through the wing when the flaps are lowered. With spoilers down, the air can not rejoin before the flaps, hast to travel a longer distance over the flaps and therefore creates more lift. In other words: The angle between cord line and relative wind (angle of attack) is raised. When the spoilers go up, part of the air can actually travel through the gap, decreasing the angle of attack, therefore decreasing the lift on that side of the wing and therefore helping out the not so effective aileron on the wing.
I hope this makes stuff a little more clear, and you didn't get bored reading through!