When a recipe calls for the separation of the whites and the yolks, it is usually to make the best of the qualities of each of the egg's components. When you beat the yolks with sugar, etc., you can make a rich, creamy mixture that adds a distinctive quality to baked goods and sauces.
Whipping the whites incorporates a great deal of air and lightness to the batter. This allows the cake to rise better and other desserts to have a lighter feel. When the eggs are kept whole, the cake may still rise, but it will lose that airy quality that you can only get when you whip the whites on their own and then incorporate it into the batter with the yolks.
Of course, those who have difficulty with cholesterol will find a need to separate the whites from the yolks for a different reason. They may eliminate the yolks from the recipe altogether in order to retain the light quality that eggs give a recipe, but without the cholesterol the yolks contain.
How do you usually separate eggs? My only experience previously of separating eggs went like this: I cracked an egg, holding the yolk carefully in half the shell, letting the white drip into the bowl and keeping the yolk in the half shell. Then comes the part when I'd transfer the yolk back and forth between the two halves until all the white was in the bowl. At this point, I'd drop the yolks into a second bowl and toss the shells into the compost.
Easy enough, but the process was often less than effective, as bits of yolk sometimes dripped into the whites. Although not a catastrophe, this accidental mixture can interfere with the whites' ability to be whipped up properly.
I hadn't thought all of this was such a big deal until I found the video that has changed how I approach separating my eggs now.