iOS 7.0.6 jailbreak works, but you have to do some hex editing
Jailbreaking is the term for hacking your iOS device so you can install apps that aren't available through Apple's own App Store. Apple doesn't support the process, it can introduce stability issues, and in some cases the Genius Bar in Apple's retail stores won't honor your warranty.
If you aren't already comfortable with the jailbreak process, this isn't the time to hop in because modifying the files that handle the hack requires at least a little experience with hex editing.
You'll need the iOS 7.0.6 installer, Evasi0n7 1.0.5, and HexEdit for the Mac. With all those pieces in place, you're ready to dive into the Evasi0n7 files so you can make a change that lets the tool see iOS 7.0.6 as an updater it can work with. Redmond Pie did a great job of detailing exactly what to look for.
After that, you'll be able to install a jailbreak version of iOS 7.0.6 on your iPhone, iPad, or iPod touch just as you normally would. With great power comes great responsibility, so don't jailbreak unless you know what you're doing and have a good reason to do so.
[Thanks to TMO reader George for the heads up]