PS3 HEN (Homebrew ENabler) is a payload that implements many of the features found in Cobra payload, except LV1 patches.
HAN is an earlier payload that mainly allows the installation of "borrowed" PSN files and modify or replace some system files.
HEN is installed using the same WebKit exploit used to install HAN. The WebKit exploit was patched since FW 4.83.
HFW (Hybrid and exploitable FirmWare) is a modified version of the Official Firmware (OFW) with the exploitable WebKit files from 4.82. Therefore, if you want to install HAN or HEN you need to use OFW 4.82 or HFW 4.84 or later.
Unlike CFW, both HAN and HEN are not permanent and you need to enable them each time you start the console if you need some features (ISO & homebrews). If you enable them, you still can use your HFW as an official Firmware. And all your original PSN games already installed will continue working as usual.
Like CFW, HEN installs various custom syscalls (peek, poke, etc.) and they must be disabled before you go online.
webMAN MOD, SEN Enabler and psnpatch allow you to disable the CFW syscalls.