Cartel Dynamic Aero Carbon Stabilizer

1. To put some weight "outside the bow" to steady the aim. 
2. To balance the mass of the bow so that it reacts in the hand correctly when being shot.

It has also recently taken on the job of vibration damping. 
It is NOT primarily a damping system.

Start with just a simple long rod and imagine the bow at full draw and put a bag of sugar on the end of the rod. 
You will see that the top limb will now bend more and the bottom limb less.
OK! So now you need to counter balance that weight with perhaps a Vee bar set up, so the bow more or less balances with the long rod horizontal!

When you shoot an arrow there is an equal and opposite reaction to the force used to push the arrow forward. Some is absorbed by the mass of the bow, the rest shows as a push of the grip into your hand.

Using the pressure point of your hand in the grip as a pivot point, if the mass is not the same above the pivot point as it is below, the bow will rotate about that pivot and once again result in one limb working harder than the other.

If you turn the bow with the long rod pointing vertically upwards, put your finger round the grip at the pressure point; the bow should balance. So this is why people add a top rod. But why not turn the Vee bar so it points upwards instead of down? This will do the same job without adding weight.

For a lightweight system you would just use a long rod with a top and bottom short rod and maybe a counter balance on the inside.

Don't forget, if you have a heavy sight you may need to compensate for that on the other side of the riser.

Not the most expensive. Not the one that everybody else uses. Not the one that matches the colour of the bow... 
Do pick the one that works for your setup!

This is just very basic information, a starting point.