it is a larger way to cut 1/4 yd of fabric. There are thousands of books/patterns designed just for using FQ cuts!
They are also great for trading, gift giving, making small items like wallets, ornamtents, pin cushions, etc...FQ are a great way to start a collection of fabrics, like civil war or 1930's reproductions, novelty prints, IE: chickens, there are so many reasons to have FQ's....