ATI Catalyst Control Centre. The ATI Catalyst Control Center is a program through which you can fine tune and customize different display features of your ATI graphics card, or overclock it, or set up programmable function keys which will implement specific settings, as well as also being able to create various profiles for various usage requirements (e.g. to suit the different requirements of various games).
Down to end-user preference and requirements:
First, your graphics card will work without problems if this task is not running. Secondly, the ATI Catalyst Control Center is used primarily by gamers, by dual-display or rotated-display users, and, occasionally, by graphics designers when calibrating their monitors. Most other types of users do not need it and do not use it. If you are in the latter category, on some PCs you can disable this task on the Startups tab, or, alternatively, you can right-click the icon in the System Tray and configure the Catalyst Control Centre not to start up at Windows boot-up.