Spiritual Pressure is Reiatsu released by the user in order to show a display of power to an opponent, and even weaken him/her, making more difficult for the latter to fight. Most Ninja and Shinigami, even Quincies and Arrancars can manipulate their release of their spiritual pressure. The most powerful Ninja such as Hikaru "Shadow" Kurosaki, Byakko Kurohitsugi, Seireitou Hyuga, Ryun Uchiha, Minkai Zokatakei, Haizo Hyuga and others have vast amounts of Spiritual Energy, which they can emit in the form of Spiritual Pressure with devastating effects.
As stated by Byakko, spiritual pressure is important in battle. When two spiritual pressures collide, the weaker one is pushed down, casuing that side to be weaker. When this occurs, the person with the higher spiritual pressure can easily overcome the opponent, as shown in Seireitou and Byakko's fight, when Byakko had the higher spiritual pressure and was able to cut through KyuubiTaishou with his Hakurei as if it was butter.