The quote in the title of this post should be the maxim of everyone who is trying to gain a technical understanding of anything.
There are a number of variants, and they're attributed to Albert Einstein, Richard Feynman, Lord Rutherford of Nelson and others. No one really knows who said it first but the concept is one that's been adopted by people striving for competence throughout the ages.
The key to this quote for me is the your grandmother part. Why does the quote use "your grandmother"? Why doesn't it say that you should be able to explain something to your next door neighbor, or your husband, or the mail man?
Is this quote trying to denigrate poor old granny? Is it trying to imply that your grandmother is the dumbest person you know, so if you can explain something to that thick old biddy then you can explain it to anyone? I don't think so.
I believe that "your grandmother" is perfect here for two reasons.
First, your grandmother is YOUR grandmother. She's genetically one of your closest relatives! That means it's likely that she probably has about the same natural intelligence as you do! Maybe her mind is a little withered thanks to her age, but it's unlikely that you would have an IQ of 200 and your second closest direct ancestor is a complete dullard!
The other thing is, that each generation tends to receive more and more education. So while your grandmother probably has about the same brain capacity as you do, she probably hasn't had as much training or experience in your chosen field as you.
Second, the other aspect that is unique to a loving, doting, caring grandma is that she's interested in everything you have to say. If you are lucky enough to have a grandmother like mine, you'll know that you're the most precious, wonderful and spoilable fellow or lass in the world to her. She always wants to hear what you've been doing, where you've been, and what you're thinking! She loves spending time with you and listening to you talk.
In essence the quote is saying "You should be able to explain something to someone who is about as smart as you are and hasn't had training in your field, but they're interested in what you have to say."
It's very difficult to explain something to someone who just isn't naturally intelligent enough to grasp it. It's even harder to explain something to someone who isn't interested in what you're saying.
For all those reasons I think that being able to explain something to Nan is the best way to know that you've understood it.
