dimensional analysis - What do units like joule * seconds imply?

I can easily understand what divisive units imply, but not what multiplicative units imply.

What I mean is, when I read "$12 \:\mathrm{eggs/carton}$", I mentally convert it to, "There are 12 eggs for each carton". I get that.

But, when I see units like joules * seconds, $\:\mathrm{J \cdot s}$, it really bothers me for some reason. I'm not sure what it's saying. It's not saying the amount of joules expended over a certain time-frame, otherwise it would be joules/second, wouldn't it? So, when I read units like joules * second, I try to relate it to my egg-carton analogy, and it comes out like this:

"There are 12 eggs for each reciprocal of a carton."

It just doesn't make any sense for me. Is this a problem for anybody else? Should this be on math SE? Is this even a valid question or am I just asking why $2 + 2 = 4$?