Shellshock refers to a set of vulnerabilities discovered in late summer 2014 that affects Bash (Bourne again shell), a command line shell program used on all Linux systems and almost all UNIX systems, including Mac OSX. If Bash on your system is still vulnerable it could allow an attacker to take control of parts of your systems and run potentially harmful programs by manipulating the environment variables using this Bash vulnerability.
Fortunately, it is fairly easy to check whether your system is vulnerable, and just as easy to fix it. Just run this one command to test your system:
curl https://shellshocker.net/shellshock_test.sh | bash
This is provided by Shellshocker.net, which allows you to easily check your system for the shellshock vulnerability and provides detailed information about it, and how to fix it. The command simply downloads and runs their shellshock_test.sh bash script that probes your installation for all known vulnerabilities and tells you if you're vulnerable and to which. They list the commands that this script will run on the site, and you can also inspect the script's code by opening it in a text editor.
If you are vulnerable it just means you need to upgrade Bash on your system to the latest patched version, or apply provided patches. On most Linux distributions just a simple security update should do the trick or you could opt to update only Bash specifically. Here are example update commands for popular distributions:
yum update bash -y
apt-get update; apt-get install --only-upgrade bash
More detailed information including how to build from source if you want to take that route are available at Shellshocker.net.
If you are on Mac OSX you just need to install a patch Apple made available for Mavericks, Mountain Lion, and Lion depending on which of these OSX versions you are on. Installing an update should be as straightforward as launching and running it.
This vulnerability shows just how plausible it is for a massive number of systems to become vulnerable due to a bug in a single ubiquitous piece of software, but more importantly, it underscores the importance of keeping your systems up to date at all times.