I want to root my phone Can anyone tell me what is the easiest way to root my phone.
I have a Samsung galaxy note 2.
And what does it mean to flash a new Rom?
There are many methods to root your device.

I just did a quick search and came up with this: http://forum.xda-developers.com/showthread.php?t=2143479. Try following that and see if it works (the process I took for rooting my tablet was pretty much just 'try every guide that I can find until something works', so really just keep looking through guides on the internet).

The term ROM is traditionally used to mean Read Only Memory. Over time, it has come to mean (in the Android world) the OS that your device runs, because the OS is thought to be read-only by some people. Flashing a new ROM just means replacing stock Android with something else.