"FTW" is internet slang for "For the win!" and is used especially to express approval or support of something. It is often added as enthusiastic emphasis to the end of a sentence. For example, "Weekend brunch FTW!" means that weekend brunch is a great thing to do.
It is important to note that "FTW" can also be used as an acronym for "fuck the world," which is an antisocial slogan. However, this usage is less common than the "For the win!" meaning.