Concentration is the ability to selectively attend to a small part of the environment for a fairly long time. This is also referred to as voluntary attention. It has a cognitive element, but is basically a biological state. In concentration, the pupils dilate, which suggests it is a type of sympathetic shift. Perceptually, concentration involves blocking out a great deal of what is happening. Concentration allows deep abstract thought, and the use of logic, so good concentrators do well academically. However heavy use of concentration tends toward a decrease in sensory acuity and empathy. That is why students who concentrate well and are academically gifted are often noted not to be athletic and not to be socially adept.
Almost always, concentrating involves blocking out the immediate perceptions and body state. Often concentration involves losing track of where one is and what one is doing. Concentrating does not have to be effortful -- losing oneself in a book "for pleasure' is concentrating. To be brought out of concentration by say an unrelated interruption or question is almost painful to a person inclined to deep concentration. Extended concentration lessens the social engagement system, and besides a sympathetic shift, perhaps strengthens the immobilization, or dorsal vagal system. However, this latter immobilization is accompanied by a dissociated rich, free, cognitive life. It may be that really deep thought is dependent on the dissociation from the immediate environment made possible by dissociation.
Admittedly an inability to concentrate (for whatever reason) may thwart sustained creativity and put one at a social disadvantage. This attentional diffusion seems to the case with ADHD, which is these days perhaps overtaking concentration as a challenge. It seems balance and flexibility is what is desirable.
The richness of concentration can have a role in innovation. However, concentration has no interpersonal or social feedback as to the groundedness of ideas. An alternative to concentration is what J. Krishnamurti called 'choiceless awareness' Most bodywork traditions work towards strengthening choiceless awareness as opposed to concentration.
A phenomenon perhaps related to concentration is self-absorption. This is the inability to really take in people and events outside oneself. Instead, one makes ideas out of outside objects, and interacts with those ideas mostly (abstraction). Other people become frustrated at being missed in some, hard-to-put-a-finger-on way. 'Energetically', the energy and attention from the core is being absorbed by a person's own thoughts and body.