So that I wouldn't accidentally touch the screen while downloading updates, my iPad was face down on the bed near me. When I inadvertently touched the back of it and moved my hand, I felt a vibration. I experimented, and found that if I did not move my hand, there was no vibration. And I thought I actually heard a faint sound when I moved my hand. After a while of examining this, I realized that it sounded like mains hum. So I unplugged the charging cable and the phenomenon stopped. Plugged the cable back in, and the phenomenon did not return. But it did return, though not as pronounced, when I picked up the tablet to enter this question.
So the question is, how can sliding fingers over the smooth outside surface of a device cause an internal vibration to come out when touching it with the same non-moving fingers doesn't? Hmmm, when I put it that way, it sounds more like a Physics question than an Apple question.