I am using ArcGIS Desktop 10.
When would one use this check box when exporting a map? I never use it, but I see it.
Here's the check box, it shows up when you're in Layout view and go to File > Export Map:
It's used to eliminate any whitespace you may have around your layout in the output file. For example, I have some MXDs set up to print on a specific paper size with specific margins, so that the maps I print can be 3-hole punched or bound without the holes affecting the map window. But sometimes I don't care about that and just want everything to fill the page. That's when you use that checkbox.
Here's the upper-left corner of a map layout with the box unchecked, my whitespace is there:
And with the box checked, it's clipped to just my map elements:
I believe ArcGIS just looks for the limits of all map elements (data frames, north arrows, any other graphics or text boxes, etc) and clips the output to that.