Mainly there are two kinds of graphics card.
Shared or Discrete.
Shared graphics card usually shares the memory with the main memory, is generally for "normal" usage like work processing, or simple stuffs.
If you are looking for long battery life for your laptop, this is also for you because usually they consume less power than discrete graphics.
Discrete graphics card usually have their own memory and can perform more graphics intensive tasks or 3D.
How about having Both!
In newer laptop, some manufacturer gives u the benefit of both worlds! Both Shared and discrete graphics are available!
To save battery/power, use the shared graphics, to do more graphics intensive stuff, simply switch to the discrete graphics!
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If your computer is fitted with ATI graphics, you may have access to ATI PowerXpress(tm) this allows u to switch graphics card easily!
IF you decide to use this feature to switch from a high performance graphics to power saving graphics. your computer performance may take a hit.
Your Windows experience index score may drop.
From 5.0 to 4.1!
More about ATI PowerXpress™