Yeah, the Downforce method is used more in Sports Car.
I don't really know much other than, it's basically a method to create a force on the car from top so that when a car moves at really high speed, it doesn't end you getting lift off the ground.
Basically it helps the tires of the car be in constant contact with the ground surface. Since moving in high speed cause to get slight elevated because of the upward lift pressure created by the wind (the faster a car moves the higher the lift force gets).
Well, if you have ridden in a car that's moving at a really high speed, you would kind-off feel the lift as car starts to shake a lot less and feels like it's driving more smoothly.
Its exactly the same principles as airplane wings, just upside down. You try to get low pressure below the car and high pressure above the car. The grip of a tyre increases with vertical load, and while you do get more grip force generated with a heavier car, you lose overall because now you need even more force to accelerate that extra weight. Downforce on the other hand increases the vertical load without increasing weight, so you get more grip without the weight penalty (you will increase drag though, which limits top speed).
Downforce isn't really used to keep the tyres in contact with the ground, that is the job of the suspension. =)
And the reason why most cars without added wings or other features generate lift, is because the basic shape of a car approximates an airplane's wing: Flat bottom and a rounded top. This tends to create a high pressure area underneath the car, while the air flowing over it is at a lower pressure, hence lift.
Also to some extent the fact that the body of the car is above the wheels will mean that the drag from the air will want to make the car lean backwards, which reduces the load at the front and increases it at the rear, making the steering feel light and vague.
These forces work at all speeds, not just high speeds, but they grow by the square of the speed, i.e. speed doubles = drag and lift(or downforce) quadruple, so the effect becomes more noticeable at higher speeds.
I deal with this stuff a lot... =)