From what I understand (please someone correct me if I am wrong), +P stands for PLUS PROOF. Proof (I think) would be the SAAMI or manufacturers (not exactly sure which) absolute limits of what the paricular firearm can stand as far as chamber pressures go. In other words, I think that +P are "test" pressures.
+P+ is obviously an even higher pressure for that particular cartridge.
Actually, no. The +P designation indicates a cartridge who's pressures exceed that of the SAAMI standards for the cartridge by about 2000-3000 psi. One reason for this designation is to prevent chambering these cartridges in older guns which may not have heat treated cylinders or were not built to handle higher pressures.
The +P+ designation indicates a cartridge who's pressures are higher than +P and there is no upper limit on what those pressures can be. For example, The .38 special's SAAMI limit is 17,000 psi and .357 Mag is 35,000 psi. A .38 +P SAAMI standard is 20,000 psi, however a +P+ could be closer to the 35,000 psi .357 mag level (it could be
but that would be stupid of the maker).