Jail breaking is setting the phone free, so you can do things with it that apple never wanted to allow.
You can have lots of tweaks and new features, many current features on the iPhone were out way before on jailbroken devices such as multitasking and lock screen notifications.
You can get apps for free, the same piracy laws apply...
I use iblacklist to block unknown numbers and people who want me to claim on PPI. I also have a lot of shortcuts, as mentioned sbsettings, you can change the look of all menus, better security, I have a time stamp on each message, open a wider variety of attachments and videos, download music, I even have a gameboy emulator and can mirror my iPhone onto a tv (currently only YouTube when unjailbroken, and only with official apple cable)
Jailbreaking is safe, in fact, they release patches for exploits usually faster than apple, it does technically void your warranty however, you can restore at any time and is untraceable.
In all, it makes your phone as customisable as android, with the beauty and reliability of apple. I wouldn't buy android, but wouldn't buy an iPhone of I couldn't jailbreak...
Also, the new jailbreak will not work on ATV3, this has been confirmed, although they are looking into it, the hardware difference is causing a delay. Every device that can operate iOS 6, including ATV2 will be untethered jailbreak, 22 devices in all.