I'm just start using ubuntu, a few months but just for fun (having a diferent SO, :)...) but now I want to improve and understand some things:
when I installed ubuntu 13, it came with a "gallium 0.4 on amd cedar" and I would like to know if this is the correct driver for my graphic (my pc: hp i5 ati-mobility radeon) or if I have to install a correct driver and Install a Graphic driver is it really necessary for some softwares in this OS?
Ubuntu is ready to use from the very first moment that you boot. Normally there isn't need to install other drivers (or modules) after installation (unless some really corner cases, I never installed another drivers).
"gallium 0.4 on amd cedar" is a code name for the mesa driver. Mesa is the library that allows software to use OpenGL and HWA capabilities of the graphics cards. Most likely your real driver is called radeon. Unlike Windows, your system comes with the most common modules loaded and ready to use, so, yes, that is correct driver for your system and you most likely won't have any problem using any other software.
