A .38 Special P revolver has 20,000 pounds per square inch behind the bullet, which results in increased performance over the regular .38 Special that only has 17,000 pounds per square inch, according to Wikipedia. The term ".38 Special P" is commonly used to reference the Smith & Wesson .38 Special +P Revolver.
Wikipedia notes that Smith & Wesson developed the .38 Special revolver series to be more powerful than the Colt revolvers that were being issued to U.S. Military. The Colt revolvers were using black powder that gave off quite a bit of smoke, but Smith & Wesson developed smokeless-powder to be used in the .38 Special revolvers and give them more of a market advantage.
When Smith & Wesson developed the .38 Special +P revolver with 20,000 PSI behind the bullet, it gave the .38 Special even more stopping power. Winchester and Remington developed ammunition to be used in the .39 Special +P. Originally, this ammunition was labeled for military and police use only, but due to the popularity of the gun, it was later made available to the public. As a result of the increased stopping power, the FBI used the .38 Special +P as their standard carry firearm for many years, states Chuck Hawks as part of The Definitive Firearms Site.
In addition, the 0.38 Special +P has become a favorite of civilians wishing to carry concealed firearms and for home defense, as the recoil is easy to handle, and the sound and noise when fired indoors is manageable.