First Fastboot is an application that is available from the Android SDK. It is a separate application ran on your computer to communicate with your device thru the bootloader.
I think the question your probably asking is if you should leave your bootloader locked or unlocked. If it is already unlocked, leave it. You can always lock it back up in the event you need to have your device serviced or sold. I say this because normally on most devices when you unlock the bootloader it wipes the device, so if its already unlocked then just leave it. My opinion.
You got WAAAAAAAY to technical for the OP. Fastboot setting in the menu is like a "quick on" if you will. It doesn't fully shut down the device. So on shutdowns and reboots, the phone will load up much faster. But with that being said, It doesn't get a memory clear or any of the good stuff that can be resolved with a reboot. Fastboot does not allow the phone to reboot. So if you are having lag issues or any glitches turn fastboot off and get a good reboot.
I only use fastboot when changing out batteries. If I have a low battery and am popping in my spare, i'll turn on fastboot before powering down so that way the phone "hopefully" restarts faster. Not sure if pulling the battery gives the reboot or not, but it's what I do. I shut the phone down almost daily for a reboot anyway to keep performance tip top.
On a side note, I do find I get better battery life throughout the day if the phone charges in the power off mode rather than being turned on.