Concentrations is this games' version of bullettime, and can be pressed with the default Q key. You need to be in bullettime/concentration for the equivalent of 15 real time minutes.
In my own personal experience, this takes into the New Game Plus form of the game, aka a 2nd playthrough. You being able to use concentration also becomes more frequent and longer as you unlock skills in the game relating to concentration.
Skills that deal with time/increasing concentration include:
Cold Blooded - More Concentration in the Bar. Be even more focused. Concentration will last for +50% longer - when you use it, the bar will dissipate at a slower rate.
By the Numbers - Concentration for Combos. Take out a couple of enemies in a row to regain your focus. Your concentration bar will completely refill after reaching a combo level that is a multiple of 6.
Headhunter - More Concentration for Headshots. Make some headshots to increase your focus. For each headshot delivered, you will receive 50% more concentration than normally.
Waste Not - Higher Combos in Concentration. Be even more efficient when focused. The combo multiplier in concentration will stack by 2 levels instead of 1 every time you perform a successful kill. Higher combos mean more experience!
Come Closer - More Concentration for Full Blasts. Do some close and personal killing to be more focused. For each close shotgun kill you deliver you will receive twice as much concentration as usual.