Before restoring (or even on a regular basis), you would create a backup of your device prior to restoring so that you won't have to start from scratch all over again. On a regular basis, especially if you have constant changes to your device like new photos or videos every week or day, it's recommended that you create a backup anyways even if you're not planning to or have no plans of restoring any time soon, this is just there as a just-in-case or God-forbid situation.
When restoring your device, (especially jailbroken devices), you'll need to DFU the device to make sure that any current constraints are bypassed so that iTunes can install a fresh copy of iOS onto it. For Evasi0n jailbroken devices, a regular restore won't work, nor does OTA update work because of a built-in mechanism from the jailbreak that prevents it, therefore, you'll need DFU mode to do so.
And do note that iOS 6.1.3 does NOT have an untethered jailbreak unless you're on the old bootrom 3GS. The new bootrom 3GS and the iPhone 4 does have a tethered jailbreak, but the 4S and 5 has no jailbreak whatsoever, so do keep that mind