I will not explain in technical details how yesterday's freshly released Bash Bug exploit works as there are already millions of articles spreading like wild fire on this subject. But in a nutshell, the problem is that while it's okay to define a function in an environment variable, bash is not supposed to execute the code after it.
Let me give you an easy example to determine whether my Bash version is impacted or not by this vulnerability. If I run the code below, I should get echoed "Vulnerable" if indeed I am:
The patch has been released yesterday so there's no excuse in not fixing your servers. Additionally RedHat/Centos/Fedora/Debian/Ubuntu and the likes, have updated their bash package as well. Updating bash will make the previous code not able to run any commands after the function: