Administration is a summed up as Paper work. Sadly this is very cosmetic understanding of the value of "paper work" or what falls under paper work. I would push the meaning farther, particularly taking stuff that I've learned in management. Between Leadership and Administration, Administration is Organization while Leadership is cohesion.
There is something about these two skill that must be taken of note, they are passive. What I mean passive is that, these skills are automatically in play and always acted upon by the Characters. A character with a high administration is organized, he or she will be easy to understand, will have the documents and data needed when the circumstance requires it, and has very good habits when it comes to keeping things organized in work.
In GURPS, you roll Administration to get the right "paper work" and sort your way out of the "Bureaucracy". Administration is also a social skill, allowing you to deal with bureaucrats. Although there is nothing in these two uses, the logic kinda twists a bit. Why does paper work mastery allow you to be chummy with a bureaucrat? Its really about procedure and using the right channels, if this is really what Administration is about then there is some conflicts, particularly the previous iteration of the skill in 3e, where it was bureaucracy.
In my experience, the skill of using the right channels and forms, and following protocol is found in Profession (specify), NOT in general Administration. These maters are very different per industry, profession, and group and Administration is a general skill that carries over different industries. (Although I would emphasize as a GM that admin has a familiarity penalty equal if you don't have a Professional skills of 12 or higher).
In my opinion as a Passive Skill, Administration measures the workload you can take on. In a 40 hour work week, it is how efficiently you can cram stuff to do for work. The only time its not a passive skill is when it is used as a Monthly professional roll for a Management Character.
A character with high Administration has the habits and professional ability to handle a variety of different topics without being distracted or having to turn his head around too much when the new problem or tasks is so different from the last. Or, the character with a High Administration can identify all the key tasks and allocate enough hours to succeed in them sufficiently.
Basically in a 40 hour (depends in the character's work week, some character can have 50 to 60 hours work week because of their own trade offs.), when you have very differing projects or tasks you can give these a 50% time penalty. In a given week, every different project from the one the character has the greatest familiarity takes on a 50% time penalty. Admin-5 is the number of tasks the character can bring down the penalty to 25%.
Edit: changing the formula so that every point counts, instead of every 2 points. to show an investment of 2 or 4cp equal to 800hours to 1600hours of practice has an impact. Basically Admin is the skill that allows you to discount the time it takes to prepare for a new task, a no. of times a week equal to Admin-5. Time to prepare is at the default 50% the time it takes to perform the action, following the rule of thumb it takes 1/3 of one's time to prepare and plan given the entire budget of an action. With Admin, you discount that by 50%.
So you have 6 key tasks in a week that would normally take up 4 hours. since you have to break your momentum to do a different task, call a new set of people, read a new set of data and research output, deal with a new set of benchmarks etc... every task from the first is going to take 50% more time. without administration or at default, a character with IQ 12, which is Admin-7, can only reduce the time for 2 tasks. So 2 tasks will only take 5 vs 6 hours (10 hours, 30 hours left), then the character will spend 6 hours on the other tasks, which basicaly makes for a total of 7 tasks in the 40 hour week no time to spare. If the character fails in one of the task, this task might eat up more time or has to be done again from scratch.
A character with Admin-12 can have 7 tasks eat up 5 hours instead of 6 hours. Thats 35 hours for 7 tasks, and 5 hours left of free time. If there was a 7 task expectation per week, then the character has 5 hours to spare. Consider it a buffer for failing in some of the week's tasks.
if you want to detail the character's actions and duties, check out the words per minute for writing, reading/researching, and composing of complex subject mater. Meetings and team discussions fit the 4 hour rule because thats the typical mental endurance average for individuals, after that amount of time information input becomes less efficient (admin determines the number of participants in such a discussion equal to Admin-5 that do not suffer any penalty). two-to-one discussions half the amount of time, 2 hours is enough to cover all the topics pertinent in most working conditions.
Admin is the skill set you can use to describe real world management skills. Although in the real world, people that organized are rare, even amongst the high positions. Usually Secretaries or Personal Assistants have Admin at 12 and above. The secretary who basically "manages" your work load to get you to be as efficient as possible is more common than a leader having the skill in high marks. In my experience most of everyone who has enough skill to be organize to get by in their work has only spent 1cp (enough to negate the 4 points penalty of default). The reason why No-one kills/has awesome stats, in Admin is that there are trade-offs and its cheaper to higher a secretary/PA to be the one organizing things. I could be increasing my merchant skill or professional skill (which more directly affects income in some cases).
In TV Donna, Harvey's Secretary in Suits, is one of those characters that have a High Admin. Since the settings is a bit cinematic reality, she is at the 13-14 level. Characters in Burn Notice has high admin, by the amount of paper work and work they fit in the few days of an episode. In the Good Wife, Carey Agos has a very high admin, allowing him to produce the most billable hours for the company. Harvey, of suits, also has a high admin if the 36 cases a day average of his work experience in the DA's office is any indication of high work output. I can't say Mike of Suits has a high admin, his Photographic memory and 100% comprehension speed reading* just makes him a monster in getting work done.
*reason why i find it very cinematic, plus the misunderstanding of how real photographic memory works.
... whoah i rambled on about Admin. I'll try to cover Leadership in another post.