Well the truth is, it’s the computer that you don’t want to zap because of static electricity (ESD) not you ;-}
Lets say you leave your PC plugged into the AC outlet but have the power switched off. As you have a three pronged power cord and you’ve plugged the cord into a properly grounded outlet the case is then bonded to ground via the cord. So by placing your hand on the cases metal frame you’ve effectively discharged your self to ground. But the objects you have on the wooden work surface can also have a static charge so if you touch one or more of them you could acquire a static charge from them so if you have removed your hand from the case and then touched a sensitive ESD part you could damage it without realizing it. You would also not want to move as well as your feet rubbing on the floor could likewise build a charge.
So by holding the case with one hand you are assured of not zapping anything. But, of course that is a real pain! So this is where an ESD wrist Strap does the job for you!
So here’s a question for you: Is the world round or flat? But of course its round right? We’ve seen pictures from space and if you sail the ocean you clearly loose sight of the shoreline because of the curvature. Well, there are people who don’t believe this! Because they haven’t seen it, it must not be true: Here are 10 ‘proofs’ that the Earth is actually flat, not round
So what does this have to do with ESD? Surprisingly a lot! Most people are also in denial that ESD is real! You can’t see it unless it’s a large charge when you reach for a light switch when you are likely see and maybe even feel a zap.
What makes this harder to understand is the relative humidity where you are working has a big bearing on how much static there is. So in the middle of the winter where I live static is a big problem, but, like today in the summer its very humid and even with an AC running the humidity is still quite high so the risk is diminished from what I would face in the winter. But, Its still there! Some components are more sensitive the ESD damage than others and some components like chips have been hardened to help minimize the damage. The damage is not always seen right away just like bending a paperclip once the clip still works but the metal is fatigued and does not have the same strength as it once did. This is the risk with a zap as it might be a week or more before the damage effects things.
So what the right thing to do? When swapping out boards, RAM or Drives in a desktop using an ESD strap is all you need.
If you are working on a logic board soldering something then you want a proper ESD mat and strap connected to the ground pin of the outlet.
In both cases you don’t want to move about and you want your tools to be on the mat or be independently grounded.