What does Prec@1 in fastText mean?
Its "Precision at 1", or how often the highest ranked document is relevant:

http://ir-ratio.blogspot.co.uk/2012/03/precision-at-1-and-reciprocal-rank.html

Suppose you are looking for items about monkeys. Your query engine queries documents for "monkeys" and ranks by relevance. If the highest ranked document is indeed about monkeys, then that's a win for your query algorithm. But if the highest ranked document is ranked 1 because it has the text "Enough of your monkey business" then its a loss, because that's not really about monkeys. 

Repeat over a bunch of search terms. The Precision-at-one is then the number of wins over the total number of search terms tried.