In addition to what's already been said... it's a bit dependent on caliber.
SAAMI only recognizes a +P variant for a handful of cartridges: 9mm Luger / Parabellum, .38 Special, .38 Super (more about this in a bit), and .45ACP. FWIW SAAMI stands for the Sporting Arms & Ammunition Manufacturing Institute, the voluntary organization that sets firearm standards in the USA. (The equivalent European standardization organization is the C.I.P., which sets slightly different pressure standards for some cartridges, and AFAIK does not recognize +P.)
.38 Super is officially always designated as +P because it's dimensionally identical to the earlier and less powerful .38ACP cartridge, but it's loaded to pressures high enough to damage some .38ACP guns. (Please note that .38ACP is not
the same thing as .380ACP!)
9mm+P+ has its roots in older European and Israeli ammo that was loaded to extra-high pressure for use in submachine guns and carbines. Very few gunmakers endorse the use of +P+ in their pistols, officially or otherwise, and using it may void the pistol's warranty. This has often been a touchy subject when it's come up in the "Semi-Automatic" subforum, so I don't want to discuss it much more than that.
As Jim Watson correctly states, .38Spl+P+ basically started out as a legal sham to allow cops and security guards to use ammo comparable to .357Mag in jurisdictions that officially disallowed "Magnum" calibers.
This ammo should only be fired in Magnum revolvers. However, as you might imagine, many authorities figured out this fraud years ago, and this fact- together with the general switch to autoloaders- has caused all but one company to drop this ammo from their product lines.
.45 Colt+P is basically synonymous with a "Ruger Only" (sometimes "Ruger & Freedom Arms") load. These are higher-powered loads that are not suitable for weaker and/or older .45 Colt revolvers.
.380ACP+P and .40S&W+P are recent marketing gimmicks used by a handful of high-end defensive ammo makers. It's open to debate whether these loads are safe to use in, well, anything.
The same warranty disclaimers for 9mm+P+ apply.
.44 Special +P is a colloquial designation for a .44 Magnum load that's optimized for low(er) muzzle flash, recoil, and noise when fired from a short barrel. There is a BIG power jump between .44Spl and standard .44Mag, and the latter can be temporarily blinding and permanently
deafening when fired indoors from a 4" or shorter barrel.
Consequently, many shooters prefer to use lower-powered .44Spl ammo in these guns, and the +P version gives them performance a little closer to .44Mag without having to step up to the full-bore version. .44Spl+P should generally be used only in .44Mag revolvers.
Hope this helps.