The most I have concentrated is during MMORPG games during PvP battles. So, I guess it's the need to win in real-time. It's like playing sports (dexterity of the hand, concentration on all sorts of indicators on the screen, assessing your enemy's state, etc.) sitting on a chair.
Cleanliness. When my desk is exactly as I like it, my laptop in perfect functioning state, the bay window of my bedroom looking out to a bright day, all surfaces of my room clean and tidy, I feel most able to work. If these things are not the case, it's an added difficulty. Of course the problem is that preparing to focus may be good for me, but it often just allows me to focus on anything, not on what I actually need to focus on.
NO PEOPLE around me. And space to work. Two things the school system does not provide.
PS: the <rant> element will never be deprecated. It's too widely used and CSS doesn't have a viable alternative yet.
Space, no people, a spacious work area, and a comfortable chair.
I can concentrate well with people in a classroom setting doing busywork (mostly because my hands just write crap down and my head is somewhere else), but for total creative concentration that makes two hours seem like 30 minutes, I can't have any people interrupting me. If I can get into that "zone," the house could be on fire and I won't notice.
MMORPG games where I have to concentrate on my hand's dexterity, assess my enemies, look at my potions/buffs and weapons, etc. It stimulated my mind for hours together. If those were a real sport, I could be one of the most dedicated sportsperson.
multitasking; breaking the focus down into set agendas that could be achieved independently or at once... concentrating on just one task tends to ensure greater burn out for me.
although if I'm procrastinating from something else of greater importance but no aching deadline overhead... that too has been known to help.
as well as...
taking a couple cleansing breaths, adopting a meditative stance and channeling all my erratic thoughts and repressed emotions into a fine point for the sole purpose of setting my universe on fire, conducting a choir of screams and connecting with my inner child by making 'angels' from the apocalyptic ashes on the ground...
A clean environment with white noise, multitasking, being interested in what I'm doing, or or something meditative and repetitive that I can get into, this website (something with systems that my Ti can get lost in)...
And dance music gets me in the mood for pretty much anything.
I think "getting absorbed" is a better term than concentration.
like many people have said, space, no people, clean working area, comfortable chair, and "white noise." To that, I'd add, a place where I only go to work (except that puts a barrier between me and actually getting *started* on the work - I've been meaning to go to campus Real Soon Now for two hours and counting...) and an area where I can pace and think for such things as transitions in my writing. For "white noise," I have a "no-words" station on Pandora with a mix of techno, dance, classical, and especially Renaissance choral pieces. Oh, and Indian and Middle Eastern music as well. Quite eclectic.
Nothing quite puts me in the mood like the good ol' panic-inducing stress of a deadline looming over the horizon.
As far as what makes me functionally capable of concentration... it's an elaborate balancing act. I need it to be relatively quiet, but not too quiet... good (non-florescent) lighting, a steady supply of cigarettes and coffee, and I need to be barefoot. How anyone can think properly with shoes on I will never understand.