Lead away a goat in passing
Damezumari might be a good way to understand this. In essence, it implies a hidden purpose in your moves. It could look like "just a simple one space jump" but it could (and must) have implications across the board. "Lead away a goat in passing". means that while you pass the enemy (i.e. move) you steal one of his goats.
In the natural course of things, regular moves are made. And yet, there is some sort of irresistable force he cannot contend with. And then, he realises the truth: His plans aren't working because all his goats are gone!
Goats is merely a metaphor for the 'hidden' purpose you accomplished with your 'regular' looking moves. There could be some aji you made cuttable, etc. and now you can take advantage of it. And the best part is, since it looks like you did something else, he will be taken totally by suprise when you cut off his stones. Or maybe, a ko fight which you start but let the opponent win so that he loses sente (I read about something like this in the second of Charles Matthews' ko fight series on http://gobase.org). What you did was construct a sequence which would "by the way" give you what you needed: sente.
Another way to look at it (on a simpler level) would be the idea of connecting by capturing stones,
It could also be seen as if the opponent makes a minor mistake, and it's in the middle of your plans, punish it while still setting up. You get a "goat" and still get to set up shop.