Understanding what "No" means, and being able to stop themselves from doing whatever it is are two entirely different things. I'm sure he does understand what No means when you say it, but he is simply, and developmentally appropriately, unable to stop himself from doing it anyway. As alegna wrote above, self-control and impulse control doesn't begin to get even remotely reliable until into the 3rd year. Before then, you can "train" your child to stop doing something to avoid an unpleasant consequence by using punishments like time outs or the 1, 2, 3 Magic or Love & Logic techniques, or you could just wait it out, redirect them, give alternatives, and accept that it's developmentally appropriate and keep directing towards the appropriate actions. Sure aversion therapy works (which is what punishments essentially are), but at what cost and to what end?
My children eventually learned (and/or are learning, since the second born is only 2-1/2) to control their impulses because they matured like most kids do - they're not perfect, but who is? Even I can't resist my impulses 100% of the time, KWIM...I redirect, I remove them or the item in question, I give an alternative, and am consistent with it. And my children are not the easy, laid back compliant type kids, they test and challenge like most kids do. I'd advise telling them what you WANT them to do instead of what NOT to do, because that leaves the door wide open for them to figure out something else. So "don't climb on the table" becomes "feet on the floor!" and "don't touch the dog's water" becomes, "have this water over here instead". KWIM? And repeat, repeat, repeat. Learning to control impulses is like learning anything else; we don't expect them to read and write after we read them the ABCs once, so why expect them to learn "No" so quickly?
It depends on what your goal is; for them to obey you, or for them to understand what's going on and "get it" on their own. I don't think 1, 2, 3 Magic and L&L are horrible, but I just don't see why punitive measures need to be implemented for toddlers during phases that are developmentally appropriate and usually outgrown one way or another...I've found by working with them through a phase instead of against them to extinguish a phase, the phase is over more quickly and with less stress for everyone.