Reiatsu (霊圧, Spiritual Pressure) is the physical force/pressure that a person’s Reiryoku creates when released. Most Shinigami and Arrancar, even Quincy and Bounts can manipulate the release of their Reiatsu.
Reiatsu VS Reiryoku
The difference between spiritual pressure and spiritual energy is simple:
Reiryoku is the amount of energy a being has stored within their body or soul, whereas Reiatsu is the pressure that a person’s Reiryoku exerts. In other words, Reiryoku is potential while Reiatsu is energy in use and can be sensed by other spiritually aware beings. In general, those with high levels of Reiryoku will often have the highest levels of Reiatsu also. A skilled warrior can overcome a person possessing greater Reiryoku by possessing greater Reiatsu. This is achieved by having greater control over their own spirit energy.
Different spirits have different colors of Reiatsu, and it does not depend on the character's race or power; instead, the color is determined by the owner’s personality.
Pink Spiritual energy in the shape of an angry cat.
When two spiritual beings collide, the side with weaker spiritual pressure will get hurt. (Ex: When Ichigo Kurosaki fights Captain Kenpachi Zaraki, the captain opened up the chest area of his shihakushō, and ordered Ichigo to cut him. When attacking with all his strength, Ichigo found Kenpachi uninjured, while his own hands were bleeding. As his sword that is highly concentrated for the purpose of killing, the spiritual pressure that Kenpachi subconsciously releases is much, much stronger). In this way a Shinigami with a greater amount of Reiatsu can use their own Reiatsu to harden their skin, and effectively protect themselves from attacks. Shinigami battles are battles of Reiatsu, if one possess a greater level Reiatsu then the other can be overcome completely.
Reiatsu at its most basic level can instill fear in others when it is very high (in comparison to the one feeling it). Willpower is the simplest way to fight this effect.
When Ichigo fought Kenpachi for the first time he felt it was impossible to win, making his Reiatsu far weaker than normal. Kurosaki was able to fight Zaraki only once he was able to counter with his Reiatsu.
High level of spiritual pressure can make an opponent feel as though they are being attacked though nothing is physically happening to them.
Captain Zaraki went after who he thought was the strongest of the intruders, Ichigo Kurosaki. As Ichigo and his group ran, he felt like there was a sword to his neck, following no matter how fast they ran.
Upon coming face to face with Kenpachi, Ichigo literally felt like he was just stabbed, but in reality, he simply saw just how massive Kenpachi's killing intent was.
During the fight with Szayelaporro Granz, Renji once again used spiritual pressure transferred through his blade in order to injure the Espada. His Reiatsu was able to cut his face since he was holding Zabimaru so close.
Captain Kenpachi Zaraki has consistently been shown to be able to focus his Reiatsu through his sword to create powerful shockwaves, usually damaging the surrounding environment as he does so. This use only occurs when the user is releasing a large amount of energy at once or in an emotional state.
In high enough quantities, spiritual pressure can be lethal to others.
After his second Hōgyoku-induced transformation, Sōsuke Aizen's Reiatsu was so powerful that it reduced a nearby Human to ash when he approached him, as well as destroying objects thrown at him.
Most characters have this form of Reiatsu, which have no other effect than those described above, along with its unique color and feeling. Most Hollows and Shinigami have this type, while every Quincy and Humans always have this type. Fullbringers are the only Humans shown to have Hollow-like powers. Yasutora Sado noticed he felt 'more at home' in Hueco Mundo, and his Reiatsu feels like a Hollow despite his species; it is still a standard type.
All Visored and Arrancar have this specific Reiatsu. For Visored, they feel more like Shinigami, while Arrancar feel more like Hollows. When Ichigo's inner Hollow started to take over Orihime Inoue could sense it, becoming afraid of how heavy and dark it was. The Visored, strangely enough, also feel more like Hollows when they release their powers. Arrancar seal their Hollow abilities, meaning they become as close to their original form as can be, explaining this phenomenon.
Three characters have been shown using elemental Reiatsu, even without releasing their Zanpakutō, or it being their natural Spiritual Power:
Fire & Heat: Genryūsai Shigekuni Yamamoto.
Captain Yamamoto has used his burning spiritual pressure to heat up his sealed Zanpakutō, causing it to glow dark orange like a recently forged sword. He has also displayed a large amount of flames emanating from his body before his Shikai, which is needed for his fire based techniques.
Ice & Cold: Rukia Kuchiki & Tōshirō Hitsugaya.
When Tōshirō was a child, he had trouble controlling his power. In his sleep, it would go out of control, affecting his grandma and causing her to shrink because of the sheer cold. This cold power caused others to fear him.