This is a somewhat complex issue, so let me start at the legal bases of it as I understand them. I'm not a lawyer and don't play one on SE either. If it is important to you, hire one and ask.
First of all, under today's copyright laws in the US (and due to a maze of international treaties, in most of the world) whenever you create some work, it automatically falls under copyright protection. That means, essentially, that nobody other than the author (or, in case the work was created for hire, whoever had it made) has the right to copy it, distribute it, or take it and create derivatives (modified versions, like bugs fixed or tranlations). A license is (as the word suggests) giving others permission to do somebody else to do some of the above. A related concept is that of public domain, works on which copyright ownership either has expired (e.g, Shakespeare's plays) or of which the author explicitly donated the rights to the public (AFAIU, this last is a US-only legal situation). So if you are legally using a piece of software, it is by explicit permission (i.e., license) or because it really belongs to you (public domain). Apart of the copyright on a specific piece of work, there are copyrights on collections. So, if I put together a collection of, say, folk songs (presumably very old, and in the public domain), the selection and arrangement is still under copyright protection. So somebody could copy the individual songs, but not copy the whole collection.
For more on the different licenses in use, look at Wikipedia on open source, or ask Google.
In the specific case of Red Hat Enterprise Linux, the individual pieces are under a hodgepodge of licenses, much is GPL, but there are pieces under BSD style licenses, the LaTeX Project License, Apache, and a long list of others. The collection itself is under GPL. Under GPL (but not under other of the many licenses), whoever gets binaries is free to distribute them further, and moreover anybody who gets binaries is entitled to full source code to the program. Note that only who gets the binaries is entitled by the licence to the sources. What Red Hat does is to publish all sources (even for non-GPL parts) of the distribution for anybody to take (the sources are here or thereabouts, depending on the exact version of the distribution). Furthermore, Red Hat acquired a few companies (for example, Qumranet in 2008, which developed tools for use with KVM, and released the under GPL) or rights to pieces of software (like the Netscape LDAP Server, which it liberated under GPL in 2005, today as 389 Directory Server). There are also pieces developed in-house by Red Hat (like RPM), which have also been made into open source. A few pieces of the distribution are deemed trade marks (you can't use the Red Hat name or logo except by permission), Red Hat segregates everything that is part of the trademark in simple packages, and gives explicit instructions on how to replace them with your own (as done by the clone distributions, like CentOS). You can get binaries from Red Hat under a maintenance contract, or sources for free, and also instructions and tools needed to put a modified distribution together. Note that this goes several steps beyond what Red Hat is required to do under current legislation and the relevant licenses. They know very well that they depend on the good will of the open source community, and benefit off it.
Red Hat sponsors the (mostly) independent Fedora project, a community-driven distribution which strives to get the best and latest of open source into the hands of enthusiasts in form of a easy to use package. Fedora is commited to work with upstream projects and open collaboration with other distributions, recognizing that going on their own means an unmanageable burden of maintaining their own forks. In turn, Red Hat Enterprise Linux starts essentially as a branch off Fedora, selecting packages, tweaking configuration, and stabilizing/hardening, and finally maintaining the versions selected by bug fixes and backports. Many Red Hat employees are active in Fedora as package maintainers, or working on external packages. Several high-profile kernel hackers are on Red Hat's payroll, while other employees are lead developers of independent open source projects as part of their jobs.