Picture of Jailbreaking iPod 4th 6.1.5 Tethered
Jailbreaking is a type of software hack that can let you do things that apple restricts you from doing. This can remove security though and not cooperate with applications or the app store. This also can lower your battery on your device as well so if you need battery this is not for you. This will let you do things like change status bar, customize your home screen or lock screen , get cool effects , record your screen and many more!  

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Step 1: Explaining Differences between Tethered & Untethered

Picture of Explaining Differences between Tethered & Untethered
Tethered & untethered are the most common asked things when someone is planning to jailbreak. Tethered is a jailbreak that needs a computer when your device is shut off. This is confusing but for some devices , you can turn it on or it will not. I have not experienced it not turning on but it it doesn't chances are its in DFU mode. DFU mode is something that makes the device vulnerable to hacks, I often mix these up with recovery but they all really do the same in my opinion.

Untethered is where you can turn your device off and the jailbreak still works, which is not available at this time due to all the security on ios 6 that hacking teams are trying to crack and find exploits, tho 6.2 and under allowed untethered thanks to the evasion team!  

Step 2: Required Files

Picture of Required Files
Now these files may not make sense to you but they will work for this. I recommend backing up your device before doing this.

iOS 6.0(NOTHING ABOVE OR BELOW CRUCIAL!) : http://www.felixbruns.de/iPod/firmware/

And for this, the tool being used will be Redsn0w (a common tool in the jailbreaking world)

http://www.redsn0w.us/2010/03/download-direct-links-jailbreak-guides.html (latest version recommeded!)