+P on a headstamp denotes ammo that is loaded to higher pressures, with resulting higher velocities. These higher pressures are held within stardard SAAMI limits, and these loads are generally to be used in stronger, modern firearms.
In respect to 9mm, with which I have the most experience, here's what I know and my first hand experiences with +P and +P+ ammo:
standard pressure 9mm-37400psi max
9mm +P-38500psi max
9mm NATO-42000 psi max
9mm +P+- no official SAAMI limit, usually midway between standard and NATO pressure (on boxes of 115gr. +P+ Speer GDHP it lists 40000CUP or 22% higher than SAAMI standard (approx. 45628psi)
What does this mean to velocities? From my Glock 17, here's what the loads look like over a chronograph:
Standard 9mm:
WIN WWB 115gr. JHP-1230fps
PMC 124gr. Starfire JHP-1140fps
REM 147gr. BJHP-1015fps
9mm +P
SPEER 124gr. +P GDHP-1245fps
COR-BON 115gr. +P JHP-1355fps
9x19mm NATO
IVI 124gr. FMJ-1285fps
9mm+P+
FED 124gr. +P+ Hydra-Shok-1205fps
WIN 127gr. Ranger T-1265fps
SPEER 115gr. GDHP-1385fps
With +P ammo you get more slide velocity, recoil and flash, with +P+ it is more pronouced. Follow up shots are slower, you need more training to get used of the added recoil and flash, especially in low light situations. Some loads use better use of flash retardant powders, but at +P+ levels there is going to be some flash and recoil! In fact, the Speer 115gr. +P+ GDHP produces more energy than any 165gr. or 180gr. .40S&W JHP load I have ever tested, not that energy is everything!
To my knowledge there is only one +P .40S&W load, the COR-BON 135gr. JHP. It screams out at 1385fps out of my G22. .38 Special make good use of +P loads, but I have no experience with this load. Maybe some wheelgunners can chime in with tech data on +P numbers for .38's. Same basic principle though as 9mm and all other calibres that utilize +P loadings.
Hope this helps.