I have no idea what the "P" stands for. I would assume is stands for "powder" or "POW!". +P and +P+ are often used by different manufacturer's to label a round that is loaded to higher pressure than their normal offering in that caliber/weight.
+P is regulated by industry standards, meaning there is a max amount of pressure for a +P in a certain caliber and manufacturers shouldn't exceed it. +P+ isn't recognized by industry standard and is a label certain manufacturers use. Also, some loads boxed as regular loads are hotter than some +P loads from other folks, and sometimes within the same brand. There is no rhyme or reason.
In general, +P means is supposed to mean hotter than regular. +P+ is supposed to mean it's hotter than +P.
This is all based off memory. So I could be wrong.