To evaluate and sort, based on merit; to compare against all entries. Derived from the idea that the paperwork representing the best candidate will end up on top of the pile (the "stack"). Typically implies sorting the wheat from the chaff, and the sheep from the goats. The best example is any objective process for deciding who does and does not qualify for a finite number of resources:
"There are only 5 slots for pilot training. There are 10 more for navigator. There are 12 for intel. When your package is racked and stacked against the rest, you want to be at the top of the pile, or else you'll end up guarding missiles outside the gates to a silo at Minot for the next three years while an ICBM operator gets to sit inside the warmth and work on his Master's."
Likewise, the phrase can stand as a noun for the process of racking and stacking, like a synonym for "the shuffle": "My records got lost in the rack and stack--now I'll never make colonel." If you didn't notice by now, "rack and stack" is conjugated as two verbs separately: "racked and stacked," "racking and stacking," and so forth (not "rack and stacked" or "rack and stacking"). Each verb can take an object, or the phrase can: "rack 'em and stack 'em" and "rack and stack 'em" are equally valid.
Civilians may be reminded of applying for a job or for college, when there is only one opening, or there are only ten scholarships. It's not that you need a GPA above 3.9 to qualify--you just need one of the ten best GPAs. Or, as a colonel once explained it to me: "When you and your buddies are running from a bear, you don't have to outrun the bear... you just have to outrun one of your buddies."