Question: What is meant by "Enabling command line editing and vi and emacs editing modes"?

I know `vi` is an editor and have used it as well, but what and how is it related to command line editing bamboozles me. I am using bash shell and a Red Hat system essentially in command line mode to learn.

Answer: 
This refers to which keys to use to move move the cursor (and go to beginning of line, etc).

In `vi` mode use `h` (left), `j` (down), `k` (up), `l` (right)

In 'emacs mode use `Ctrl`+`F` (left), `Ctrl`+`N` (down), `Ctrl`+`P` (up), `Ctrl`+`B` (right)
The other answers are good, but just filling in a bit of background: Basically, this was an attempt to make command-line editing conform to the reflexes people had developed from using their preferred editor -- which at the time was almost always going to be either emacs or vi, both having rabid fans and detractors. 

These days, with keyboards that have dedicated Home, End, cursor, page up/down, and insert/delete keys that all editors support more-or-less similarly, the editor-specific mappings are somewhat less used and this setting matters less than it did at the time.