Nah homie, I think you got it twisted. The deep web is ANY content that is not indexed by search engines. That includes private messages, since they are not visible to Google. That's the reason why it's so large. If it was only hidden services, then it would not be so large.

Anyways it's colloquially used to refer to hidden services like tor and i2p. The only thing legit there is the CP and the drugs/guns, but be careful of scams and cops. People make fake drugs selling websites/accounts, so make sure to check their reviews before buying. If it sounds too good to be true then it probably is.

And actually there is NOT complete anonymity, because cops own a lot of the exit nodes, and they are always on the look out. People get arrested every once in a while downloading CP on the deepweb, or so I've heard.

http://en.wikipedia.org/wiki/Deep_Web