For what word representations are, see http://technology.stitchfix.com/blog/2015/03/11/word-is-wort...

Sentence classification is the generic term for bucketing sentences into different labels - those labels could be "positive", "negative" and "neutral", thus allowing for sentiment analysis.

But they could also be other labels such as "sports_news" or "finance_news". This library allows both.

Yes, it can be used for sentiment analysis.

This library basically means you don't have to write the code for sentiment analysis anymore (just one example).

Just feed it a model:

    $ ./fasttext supervised -input train.txt -output model

And then you can predict what the most likely label for a text is:

    $ ./fasttext predict model.bin test.txt

It learns word representations and sentiment classification at the same time.

Traditionally, word representations are learned by looking at surrounding words. So "good" and "bad" will have similar word representations.

By training on sentiment, similar sentiment words should be clustered together.

(Not OP) I did and it's still rather vague. I totally see where s/he's coming from with this question.