This is for situations where you don't have a strong made hand on flop - and you also don't have the pot odds to chase a backdoor draw.

Do you do it and what is the criteria that must be met in order to determine whether you would "peel one off" to see if you get a good turn card that gives you "redraws"?

In most instances it is just not worthwhile to be fishing for a draw to a redraw type of thing without odds to do so. The one case where I sometimes peel one off is when it is HU and I am out of position and I don't think the other guy has anything but is also capable of making a laydown when I CR him on the turn with likely nothing. Needless to say this is something that doesn't need to be attempted often and then only with a VERY good read of your opponent and a favorable board working in your corner.

With a hand like AK you will many times be getting correct odds to chase as the pot has usually been raised and if you miss you need a little less than 7:1 on your money to chase if you think all of your outs are good. Whether or not to continue with AK depends alot on what type of flop is out there and what kind of action you are facing, your position and several other things. Learning what to do with AK on a missed flop is one of those "experience" type situations that is hard at least for me to put in a nutshell on how to handle because what you conceive to be the correct play depends on too many variables most of the time to capture the solution in a clean synopsis.

Please define "peel one off" for me. Is it to stick around for one more card hoping to catch a draw?

I see that expression a lot, and never had a grip on it.