Gauge is the term that is used to define the proper tension you should work to insure that the crocheted piece you make will be the right size when it's completed. The hook size listed in the pattern is just the size used by the designer to work at the proper gauge. You may need to change hook size in order to work at the given gauge. It is especially important to work to the proper gauge when making garments -- anything that you want to fit properly!
Gauge is usually defined in the pattern by a ratio of stitches and rows to a given measurement such as 16 stitches and 14 rows in single crochet = 4". You should always work a swatch of fabric (approximately 4" x 4") in the stitch pattern of the piece you are making. Then count the number of stitches and rows in the measurement designated by the gauge given in the pattern. If you find that your swatch has more stitches and rows than the gauge, you are working too tightly so change to a larger hook and try again. If you have fewer stitches and rows in the area, you are working too loosely and should try a smaller hook. Keep changing hook size until you arrive at the proper gauge.