Judging by your post, it seems that this is a new computer for you, correct? ATI Catalyst is a program bundled with the drivers for your graphics processing unit (GPU) or video card. It allows you to customize how your computer displays things, and allows for other customizations. CCC.exe is the process for this program. It is similar to the NVIDIA GeForce driver program you may have had on your previous PC. If you'll look at the CCC.exe process in your task manager, you should see it running from the C:\
Program Files\ATI Technology directory (or Program Files (x86)). If its running from this directory, you should have no concern over whether or not it is a legitimate process.
Also, it is definitely good practice to keep your drivers updated for all hardware running on your PC, so there is no harm in updating this.
It is possible to remove this program, but should not be necessary. If you really want to remove this program, or would just like more information on the process, this guide should be helpful:
Hope this helps,