Make a visualization of the internal register/memory state in every step of a small program so you can see the program behavior :
To do that, you can explain first what is an register, what can of operation you can do with the register shown by a very small ASM program. (like that you can understand not only the software program concept but how it is run)
I'll say programming is a way of making life easier to anyone in a digital manner. Like providing a calculator to compute a stuff rather than providing a pen and paper.
I usually tell people what I am specifically working on, rather than some abstract "this is what programming is". I think most people understand the general concept of what a computer programmer does (in that they understand that a computer must be "programmed" in order to do anything). At least, that's been my experience when people ask me what I do.
In my particular case, I usually tell them something like "you know how radio stations have competitions where you text in your favourite song or whatever and you win a prize, well we do the backend processing on that - so all the messages come in and we collate the data and spit out the name/number of winner".
It's not a "trivial" answer, but everybody who's asked me has been able to understand it, at least on some level. I guess it does depend on the kind of programming you do, though.
You have to use examples that they can relate to. Something from their field of expertise. Make it interesting and make it relevant.