I hope that someone can explain why this was happening.

The problem I had was that the Backspace key did not work when VIM was in the "INSERT" mode. I traced the problem to the following command:
stty erase '^H'

Removing this commmand solved the problem, but i don't understadn why.

Here is what was confusing:

In the unix command line, the backspace key works fine.
In VIM, the backspace works fine for a command - :set abc <-I can backspace here and delete characters

If I go into “Insert mode” in vim, then the backspace key acts like the delete key. Pushing backspace does not move the curser left to delete characters I just entered.
ALSO – while in “insert” mode, I can delete characters using the left-arrow & backspace key (so it looks like backspace sends the 0x7f char).

Running x86_64 GNU/Linux