Room in a primary is a good thing, because you want the yeast to have enough oxygen. Oxygen = reproduction, and you want a big colony of yeast to be able to convert a large quantity of sugars relatively quickly.
Again: primary --> oxygen = good
In your secondary, however, oxygen is bad. It contributes to cardboardy flavor, I guess, which is why you want to minimize splashing and whatnot when either racking to that gorgeous 6 gal. carboy/BB, or even if you are going straight to bottles.
Again: secondary --> oxygen = bad
If you have too much headspace in your secondary (or in your bottle, esp. true for wine) it can cause off-flavors potentially, and it can hurt the aging of the beverage. If you want to rack a batch into a too-big container, find some way to displace the extra room air (which contains 20% oxygen) either with more volume (a previous batch of homebrew), solid objects that won't affect the volume or carry in microbes (boiled marbles have been suggested), or another gas which is heavier than oxygen (nitrogen is too light) and won't leave a flavor (sulfur dioxide? I dunno, but I am not planning on trying it).
My wine brewing buddy and me have been discussing a system to allow dry ice to sublimate (transform from solid to gas, without a liquid in between) in order to displace the room air in a secondary. We haven't ironed out all the kinks yet, but I'm thinking I might give it a try next half-batch I put in my carboy for a secondary.
Obligatory DON'T DO IT OR DIE warning: *enclosing* dry ice inside a container can cause explosions, damage, maiming and/or death, so it is not recommended for people I give a damn about, i.e., other homebrewers. :cross:
Dry ice releases carbon dioxide, a poisonous gas, so it should only be done in a well-ventilated area, unless you are someone I despise, in which case go ahead and play with it all you like, you sorry sap.