Red Hat, CentOS, and Fedora are three different Operating Systems that are directly related to each other due to the Red Hat company. Red Hat, or Red Hat Enterprise Linux(RHEL), is an operating system that is actively developed for by Red Hat inc., who provide support services for the OS for a fee. The OS does use some trademarked material and therefore has slightly more complicated rules surrounding its opens source status. Fedora is a community based OS that is sponsered by Red Hat and is designed to have the most recent and up to date software available. It also serves as a testing ground for future revisions of RHEL. CentOS is a fork of the RHEL and is supported by the linux community, it is designed to be similar to Red Hat but free to use.
RHEL is a more commerical oriented OS, meant to be used in a business emvironment that has needs for reliable and well supported software systems. Fedora is an OS for those who want to use the bleeding edge of Linux distro's, and try out the new features. CentOS fills the void of a business oriented OS that also removes the trademarked material from RHEL allowing for more freedom in its open source nature.