I've got a gap between leaving the military and applying to business school... how should I spend it?

Sometimes people must get out of the military earlier than they expected, and sometimes people just didn't plan for b-school far enough in advance. Either way, you may find yourself in a situation where you are getting out of the military a while prior to applying to b-school and you need to figure out how to best spend that time; mostly so that you can help and not hurt your future applications.

If you can apply while still in the military, that would likely be better for you. You don't want to seem like you just got out and didn't properly plan, and it's just more difficult to explain why you're applying shortly after leaving the military when most of your military peers are applying a year before leaving and will have a seemingly smooth transition. In short, if you can extend your military service by a bit and apply why still in uniform (even if you're on terminal leave), that is likely better.

Rule #1: Any normal job you will take will likely hurt you. Why? Working at a place like Booz Allen, SAIC, or even a company like HP or Sony lowers your cachet. Working for an even lesser known brand is even more harmful. In short, if you work for a company that is not heavily recruiting from top b-schools, then you are adding a second tier name to your resume (by elite b-school standard), and hence hurting your overall brand. I would go as far as to say that it could destroy your chances completely, because you will appear as somebody who didn't properly plan, took a "normal" job and now need an exit, even if the exit was always your plan - that can't be proven. That is simply not top b-school material.

It could in theory be ok if you work for a place like Goldman Sachs, McKinsey, or a tech job at Apple... but if you do, you are likely taking a serious step back in responsibility and taking a post-college Analyst job, which means you have effectively undermined all of your progress in the military and could now be considered similar to a 23 year old working at McKinsey. You risk applying as an "Analyst with military experience" versus just somebody who is a high trajectory leader within the military. "Interesting" jobs could be an exception to this rule: working for/with a Governor or a Chief Justice, as a foreign correspondent/reporter for a well known paper, as a Special Projects guy for a well known CEO, or in a prestigious private equity firm or hedge fund. In other words, the 0.1% of jobs that people can actually get... which is not surprising, since you are trying to place yourself in that band.

Rule #2: Doing nothing will definitely hurt you. This one should be pretty obvious. You don't want to be applying and say that you've just been hanging out watching TV and watching paint dry. Nobody who wants to go to a top b-school would want to do this anyway, but I'm just covering the basics.

So what can you do? Assuming that some super elite job is not available to you, you want to do something interesting, unique, engaging, thought provoking, intellectual, and memorable. Some simple tests for this (before I give examples):

Is it something you would tell your grandchildren about?
Is it something random people meeting you would say "tell me more about this!"
Is it something you can probably not do at any other point in your life?
Is it something that your future b-school classmates would find interesting?

If the answer was YES to all of the above, then you know you are on track. Here are some examples:

Volunteer and go work in a non-Western country. Go teach English in China, or work in a jungle preservation project in Latin America, support construction of new sanitation solutions in Africa, etc. Why? Business schools like people who stretch themselves, like to contribute to the world, are internationally engaged (just being to Iraq and Afghanistan does not count), and are able to work in diverse environments.
Write a book. Get published by a well known publisher and this would certainly help showcase new skills sets. Obviously this won't be an option for most people, but some of you are naturally gifted authors.
Just travel. Spend 6 months backpacking through 50 countries. Why? Same as above... it increases your international awareness, social skills, and worldly awareness. It says that you prefer to visit 50 countries during your 6 months off than to spend it within 50 miles of the home you grew up in, and the former tend to be the types of people who go to top business schools, not the latter.
Start a business. If you have an idea, pursue it. If you are successful, great! If not, it's an even better angle as to how you discovered you need to go to business school. Just a warning: don't start a "boring" business - this is in line with why you don't want to work for a "normal" company. In other words, don't start a new lawn cutting service in your town, or open a local bike shop. Your business should be innovative and at least target a global reach with significant impact; whether or not you get there is less important. You want the business to reflect your overarching and big picture thinking.
Enter an athletic competition. If you are a fitness nut, then this could work. This would need to a pretty high profile event, a US Championships level event. You could take 10 months to train for this event, and it would need to be something that people have heard of. Obviously actually achieving good results will be important too. You don't have to win, but if this is your main dream and you spend 10 months training for an event and then not even qualify, then it doesn't bode well for one's ability to anticipate outcomes. In other words, you need to be in it to win it (or at least come close). It would need to be something the school want want to boast about in their marketing material ("...we even have a student who recently won XYZ...").
Become an actor. Move to LA and land appearances in some TV shows or movies. Sound difficult? It is. Don't do it if you think you will have nothing to show for it. You don't want to sound like an out of work waiter in LA. That would be a big step back. However, if it's always been your dream, you might as well do what you love.

What do the above have in common?

They show ambition.
They demonstrate a campaign plan to achieve something meaningful.
They produce something that few people will ever attempt, but probably wish they could.
They reveal an inner passion of yours (volunteering, traveling, writing, athletics, acting, etc.), and your follow through on those.

There are manny other variations of the above that you can pursue, and hopefully these examples give you a good idea. Hopefully now you see why a candidate with such an experience will be seen as more attractive than somebody with a fairly boring job that most junior officers can achieve when leaving the military.