What is the Full Form of FTW ?

FTW - For The Win

"For The Win" is an internet expression which represents enthusiasm to win something. It is used to cheer for something, or recommending a particular entity in a big way. For example : I say "Nutritious Diet, FTW", it represents that i am encouraging myself for eating Nutritious Diet which help in reducing my weight.

A word of Caution : Always try to speak the full form of FTW, because it also represents a very negative meaning which is explained below. 

FTW - F**k The World

It is a negative meaning, most commonly used by anti-authoritarian and social rebels to express frustration with modern society. But now, it is getting outdated and has converted into more positive meaning "For The Win".