Soul power is an ability developed by Servants as they grow older.
Explanation
Because a servant has already died and their soul is only attached to their body by the will of a reaper, a servant can command their soul to expand beyond the confines of their mind and affect the world, especially through a channel that they already have some control over, such as their own body or the products of their powers. Because this power is imaginary, it is difficult to affect or counter with a purely physical response, but like the servant's body, it is still most definitely real enough to have a tangible impact on the world. As the servant spends more time connected to their reaper, they develop a greater and greater ability to control their soul, allowing them to use more soul power.
Development
Unlike skills and Servant powers, a servant's soul power does not vary in speed of development. Whether a servant is practicing the use of their soul every day or frozen in a jar, their soul power will always become stronger at a set rate. This means that even with a very intensive training regimen and frequent emergence a young servant will still be at a disadvantage against an older one.
Utility
The easiest thing to do with soul power is add an imaginary component to a physical attack, which will allow it to penetrate and damage the shadow of an aberration or impact a reaper. At higher levels it can also be used to make the servant's body and manifestations of their power more difficult to counteract. It can even begin to affect more abstract properties, such as making something explode with more energy than the chemical reactions acting on a given mass should allow.
Passive Soul Defenses
One useful property of extremely high levels of soul power is to automatically empower the servant's body at all times. This means that mundane threats and weaker servants will always be at a disadvantage when trying to harm the user. At about 100 years old, almost any mundane attack will become totally pointless even for inflicting temporary injuries, preventing even gunfire from leaving more than bruises.
This can also be done actively with an act of will. Doing so will make the servant more resilient than they would be otherwise, but only by a set amount. It seems likely that it is also possible to deliberately turn off this resilience, although there are few scenarios where it would be useful to do so unless trying to self-destruct.
Field Density and Soul Pressure
Another useful ability that is granted with great age is the power to make one's soul expand to fill the space around them. This accomplishes a number of things. It can make servants with dramatically weaker soul power unable to use any abilities not centered on their own body within the area of influence of a more powerful servant. It can also make anyone nearby feel awed and intimidated, especially if they do not have much soul power of their own to counter the effect. It also makes weaker servants in the area feel compelled to answer questions for the more powerful servant, although it is unknown if this is due to the intimidation or a separate effect.
Although field density and soul pressure are technically the same ability they are called different things to distinguish use. Defensive use to protect the space around one's own body is called field density, while offensive use to lock down the entire battlefield is called soul pressure.
Artificial Augmentation
While it is not possible to train soul power to make it improve faster, it is possible to create devices that can temporarily increase some parts of a user's soul power temporarily. The only known device able to do that is Hector's Magic Shield, which increases passive soul defense to the level of Abbas Saqqaf at the time that he helped to create it. However, it does not have any effect on the user's soul power outside their body, causes extreme pain when used, and can only be used for a limited time dependent on the user's age without injuring their reaper. Sazandara noted that the Magic Shield was just a prototype and that more devices like it would be made.