The game runs on real dates and real times, so if it says 13.45pm on Tuesday 4th Jan in the game, that means 13.45pm on Tuesday 4th Jan in real life.
However, to make things a bit more exciting, the game runs at 4 times regular speed, so that fighters can fight more often and will improve in skills more quickly than they would in real life.
The 4 to 1 speed of the game also means that your fighters will age more quickly, with all fighters ageing by one year every 13 weeks. As a fighter reaches his thirties he will begin to lose a step and slow down. He will lose some of his skills and will therefore become less effective.
In general, the older a fighter is, the slower he will learn new techniques in training and also the slower he will be able to improve his physical attributes through training.