Briefly, SELinux adds some new permissions to files, new contexts to users and so on, so what happens is you specify what a given context is allowed to do, to a very granular level. For example, if you take postfix, it's split up into lots of programs, so you could say that the "init" context is allowed to run the postfix startup script but none of the rest of it. The postfix startup script will convert into some "postfix startup" context which is allowed to start the various programs but nothing else. So there will be a a postfix process that allows incoming IP addresses and can send on a specific FIFO and nothing else. There is another program which can read from the FIFO, change certain files and nothing else. So, imagine if you break into the program that talks with the internet: all you can do at that point is talk with the internet and talk with the FIFO. You can't read any files, write anything, execute anything, etc.
So that's kind of the idea of it. The above assumes an extremely tight SELinux configuration and no bugs in SELinux that would allow you to break out of your context. I've never seen a configuration as tight as described above but there did use to be a guy who had a Debian linux machine running on the internet where you could log in as root and try to break stuff. As far as I know, no one ever hacked that machine, starting out as root in a bash shell.