Maai refers to the distance between things. Maai is often the single most important factor in determining the outcome of a combative encounter. It sometimes happens, for instance, that a combatant thinks he has established a favorable maai only to have it suddenly turn out to be to his opponent’s advantage.
Below a video of Nukina sensei's explanation on Kihon gumite in which he explains about maai and kiai.
Maai can also be described as space-time. After all, it is not only the space that you have to control, but the time that you are controlling the space is just as important. Distance and timing therefore can’t be separated from each other. If you observe somebody’s or your own mistakes it is often these two not corporation. Always understand that distance and timing are one. If they are not, then you are not controlling space-time. Also, it can be seen that students who often train together start to correct each other’s mistakes. You must be aware of this.
nukina - ishikawa sensei summercamp 2006
Apart from the physical maai, there is also a mental maai. Imagine a big empty hall and somebody will stand next to you. Probably you will think he stands to close to you. This same distance can feel very normal when you visit a very busy public place. This mental maai changes according to the constantly changing environment. In the dojo you should use this mental maai to put pressure on the opponent. With this pressure, you can dominate and control him. Force the opponent off-guard or force him to act (actually react). Forcing the opponent is to manipulate the maai.
PRINCIPLES
nukina - ishikawa sensei summercamp 2006